A: The Greek Emphatic Diaglott is an English translation of the portion of the Scripture which commonly (albeit incorrectly) is termed the "New Testament". The term "diaglott" means that the Scripture is presented in two languages, in a single volume; the Greek original appears side-by-side with the English translation. The assertion to which you refer is the opinion of the translator, or perhaps that of the editor or publisher of the volume; it is almost correct, but not quite.
I. Consider the passage in its entirety:
"But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises. For if that first covenant had been faultless, then should no place have been sought for the second. For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah: not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord. For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people: and they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest. For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more. In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away." -- Hebrews 8:6-13
The author of the epistle to the Hebrews cites Jeremiah 31:31-34:
"Behold, the days come, saith the Lord, that I will make a new covenant with the house of Israel, and with the house of Judah: not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the Lord: but this shall be the covenant that I will make with the house of Israel; after those days, saith the Lord, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. And they shall teach no more every man his neighbour, and every man his brother, saying, Know the Lord: for they shall all know me, from the least of them unto the greatest of them, saith the Lord: for I will forgive their iniquity, and I will remember their sin no more."
Both passages speak of the New Covenant, which is a covenant made by the Lord God with the nation of Israel as a whole, which is to say, with all thirteen tribes. The appellation, "the House of Israel" refers to the Northern Kingdom, comprised of ten tribes; the appellation, "the House of Judah" refers to the Southern Kingdom, comprised of three tribes. The claims of the contemporary Protestant Pulpit notwithstanding, the contemporary Jewish state is not in view in this passage, nor is it in view in any other passage of the Scripture; the contemporary Jewish state simply has no Scriptural legitimacy.
Jeremiah wrote circa 586 B.C., as the Chaldean army of Nebuchadnezzar, having surrounded Jerusalem, was demanding surrender of the city. When the city fell, the survivors of the siege were deported to Babylon, there to spend seventy years in captivity. More than a century and a half prior to the prophecy of Jeremiah, the nation of Israel had been divided into a Southern Kingdom comprised of the tribes of Judah, Benjamin, and Levi, and a Northern Kingdom comprised of the remaining ten tribes. Despite the division, both kingdoms remained in covenantal relationship with the Lord God under the Old Covenant. Not long after the division, the Northern Kingdom gave herself over to idolatry, for which cause she lost covenantal relationship. Subsequently, circa 721 B.C., the Assyrians invaded and carried away captive the tribes of the Northern Kingdom; those tribes never were to return to the Land of Promise.
The prophecy of Jeremiah concerning the New Covenant has in view other prophecies, such as that of Hosea, which foretell a regathering of the descendants of the divided nation, a reunification of the divided nation under one king, and an attendant restoration to covenantal relationship. This regathering began two thousand years ago, with the sermon of Peter on the Day of Pentecost; the regathering shall continue until the moment of the Resurrection. The king under which the nation is reunited is Jesus, the Christ, the Son of David. The covenant which embraces the Regathered of Israel is the New Covenant. The entity into which Israel is regathered is termed the EKKLESIA, which is a Greek word meaning an assembly of the called-out. The King James Version uses the English word "church" to translate EKKLESIA.
II. The following is a brief explanation of the relationship between Israel and the Church:
(1) The Old Covenant and the elements of the Old Covenant, including the Law of Moses, were but temporary. The Old Covenant, being a national covenant perpetuated from generation to generation with the line Abraham-Isaac-Jacob, provided benefit on the basis of physical birth, irrespective of justification.
(2) As is the case with any covenant, death terminated covenantal relationship under the Old Covenant. Moreover, inasmuch as only the Justified have the promise of resurrection to Life Everlasting, the Old Covenant could not provide benefit beyond the grave.
(3) Both the Old Covenant and the physical nation of Israel by design were temporary; each was but a shadow of a corresponding everlasting reality; but the New Covenant could not be realized apart from the death of Christ Jesus in the role of Covenant Sacrifice, Hebrews 9:16-17.
(4) Reality lies in the Spirit Realm, and not in the Natural Realm, II Corinthians 4:18, Hebrews 11:1-3. The things of the Natural Realm have an end; the things of the Spirit Realm are everlasting. The Old Covenant, which is termed "the Letter", pertains to the Natural Realm. The New Covenant, which is termed "the Spirit", pertains to the Spirit Realm.
(5) Inasmuch as the New Covenant is an everlasting covenant, those who are partakers of the New Covenant must live for evermore; this is the necessity for which the Justified are resurrected to Life Everlasting.
(6) Both the Justified who enjoyed covenantal relationship with the Lord God under the Old Covenant and the Justified who lived prior to the Old Covenant, understood the inevitability of physical death, and thus anticipated resurrection to life everlasting; clear testimony to this fact is found in Job 19:26 and in the 11th chapter of the Epistle to the Hebrews. He who has been justified by faith and is walking in the Way of Life is confident that he shall receive those things which the Lord God has promised him, and that death cannot nullify the promise nor prevent receipt of that which has been promised. Indeed, his confidence in the word of the Lord is such that he requires of the Lord no explicit assurance concerning resurrection to Life Everlasting; consider Hebrews 11:17-19. To die in faith is to die with the expectation of being awakened from death, Hebrews 11:13.
(7) Participation in the New Covenant is limited to those who have been justified by faith; they and they alone have the promise of resurrection to Life Everlasting.
(8) When Paul declares that "they are not all Israel, which are of Israel", Romans 9:6, and when Paul uses the appellation, "the Israel of God", Galatians 6:16, he is speaking of the fact that the Lord God views as true Israelites only such of the physical line Abraham-Isaac-Jacob as are justified by faith.
(9) The Protestant concept termed "Replacement Theology" is in conflict with the truth declared by Romans 9:6 and Galatians 6:16. According to Replacement Theology, the Church takes the place of Israel and becomes the recipient of the promises which the Lord God made to Abraham and to Israel. The truth of the matter is that there is that the Church does not replace Israel, for the Church IS Israel, being drawn exclusively from the physical line Abraham-Isaac-Jacob. To be precise, the Justified of Israel constitute the Church. A fact of which many students of the Scripture lose sight is that the promises which the Lord made to Abraham, Isaac, and Jacob pertain only to the Justified of Israel. Thus, Israel -- and not another entity -- is the recipient of everything which the Lord God promised Abraham, Isaac, and Jacob.
(10) All of the justified, irrespective of historical epoch, are made partakers of the New Covenant. The justified include Adam and the Woman, Abel, Seth, Noah, Shem, Abraham, Isaac, Jacob, all of the Justified of Israel of the previous era, and all of the justified who live in the present Christian era.
(11) Protestant Theology accords to the so-called "Old-Testament Saints" a resurrection status which is inferior to the status of the "Christian". But that teaching is false. The Justified or Redeemed constitute a single body, namely, the figurative Body of the Christ; in that body there is no division. All of the justified who have died, irrespective of historical epoch, today lie in the grave, awaiting resurrection. In the Resurrection, all shall be raised together, and all ever more shall be with the Lord Christ.
III. Theologians generally, together with most students of the Scripture, fail to discern that the great covenant between the Lord God and Abraham recorded in the 15th chapter of Genesis is none other than the New Covenant; consider the third chapter of Galatians. However, the covenant sacrifice prepared by Abram could not ratify the New Covenant, for it is not possible that the blood of bulls and of goats should take away sins, Hebrews 10:4. Rather, the sacrifice prepared by Abraham foreshadowed the death of Christ Jesus in the role of Covenant Sacrifice.
In the day of Abraham, a solemn covenant was ratified by a ceremony in which the parties to the covenant sacrificed animals of great value. The weight or import of the covenant was reflected by the value of the Covenant Sacrifice; consider I Peter 1:18-19. The carcasses of the animals were divided, so that the parties to the covenant might walk together between the pieces of the sacrifice, thereby declaring one to another and to witnesses, "Should I violate this covenant, may I likewise be slain and my carcass divided."
Prior to the ceremony, the Lord God caused a deep sleep to fall upon Abraham, the consequence being that the Lord God alone, taking the form of a pillar of cloud and a pillar of fire, walked between the pieces of the sacrifice. By proceeding alone, rather than in the company of Abraham, the Lord God made with Abram an unconditional covenant which imposed no demand upon Abram. In the same manifestation -- a column of cloud by day and a column of fire by night -- the Lord accompanied the Children of Israel during the forty years of wilderness sojourn.
Actual ratification of the New Covenant did not occur until the death of Jesus the Christ, Hebrews 9:15-17. The King James Version bungles the translation of Hebrews chapter 9, incorrectly rendering the Greek DIATHEKE as "testament" and DIATITHEMAI as "testator". In the epistle to the Hebrews, DIATHEKE has the meaning "covenant", and DIATITHEMAI has the meaning "covenant sacrifice".