The generation in view is the generation which with their own ears heard Jesus deliver the Olivet Discourse.
Here are the pertinent sentences of the prophecy:
Matthew 24:3 - And as he sat upon the mount of Olives, the disciples came unto him privately, saying, Tell us, when shall these things be? and what shall be the sign of thy coming, AND OF THE END OF THE WORLD?
Matthew 24:34 - Verily I say unto you, THIS GENERATION SHALL NOT PASS, TILL ALL THESE THINGS BE FULFILLED.
Matthew 24:14 - "AND THIS GOSPEL OF THE KINGDOM SHALL BE PREACHED IN ALL THE WORLD (OIKOUMENE - inhabited earth = Roman Empire) FOR A WITNESS UNTO ALL NATIONS; AND THEN SHALL THE END COME."
Mark 13:10 - AND THE GOSPEL MUST FIRST BE PUBLISHED AMONG ALL NATIONS.
Mark 13:30 - Verily I say unto you, that THIS GENERATION SHALL NOT PASS, TILL ALL THESE THINGS BE DONE.
Luke 21:32 - Verily I say unto you, THIS GENERATION SHALL NOT PASS AWAY, TILL ALL BE FULFILLED.
The prophecy was fulfilled in the days of the Apostles; to this fact attests Paul in Romans 10:13-18 and in Colossians 1:3-6:
Romans 10:13--18 - For whosoever shall call upon the name of the Lord shall be saved. How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher? And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things! But they have not all obeyed the gospel. For Esaias saith, Lord, who hath believed our report? So then faith cometh by hearing, and hearing by the word of God. But I say, HAVE THEY NOT HEARD? YES VERILY, THEIR SOUND WENT INTO ALL THE EARTH, AND THEIR WORDS UNTO THE ENDS OF THE WORLD.
Colossians 1:3--6 - We give thanks to God and the Father of our Lord Jesus Christ, praying always for you, Since we heard of your faith in Christ Jesus, and of the love which ye have to all the saints, For the hope which is laid up for you in heaven, whereof ye heard before in THE WORD OF THE TRUTH OF THE GOSPEL; WHICH IS COME UNTO YOU, AS IT IS IN ALL THE WORLD; and bringeth forth fruit, as it doth also in you, since the day ye heard of it, and knew the grace of God in truth:
Several factors are key to understanding the prophecy and its fulfillment; in essence:
(1) The phrase which in the King James Version reads "the end of the world" should be translated "the end of the era"; the Greek term AION means age. The reference is to the era of Israel as a physical nation. Under the Old Covenant, Israel was comprised of all of the descendants of the line Abraham-Isaac-Jacob, irrespective of justification. But from the time of the Resurrection of Jesus forward, the name "Israel" appertains to "the Israel of God," Galatians 6:16, which is a nation comprised exclusively of the Justified of the line Abraham-Isaac-Jacob, in the relationship of the New Covenant.
(2) The purpose of the Way of Life (and thus, the purpose of Salvation) is to qualify individuals for citizenship in the Kingdom of God. The Kingdom is a global government, and every citizen of the Kingdom is an officer of the government, John 14:2-3.
(3) Adam was created as the progenitor of a race of men from whom the Lord God might call candidates for service in the Kingdom. Mongrelization of the Adamic Race brought about the great Deluge in the day of Noah, which annihilated the Adamic Race with the exception of the family of Noah, and all of the mongrels. After the Deluge, the pool of candidates progressively was narrowed, eventually consisting solely of descendants of the line Abraham-Isaac-Jacob.
(4) The Kingdom of God first was prophesied in the Garden; since that time, every generation of the Justified has anticipated with eagerness the advent of the Kingdom.
(5) The Gospel is the "good news" or "glad tidings" (Greek, EUAGGELION) that the Kingdom has been implemented, by the session of Jesus upon the revived Throne of David, so that the Kingdom is a present reality. The Session took place twenty centuries ago, shortly after the ascension of Jesus into Heaven.
(6) Here it should be noted that the "glad tidings" would not be glad were it the case that, according to the expectation of the Protestant, implementation of the Kingdom lies yet in the distant future. This explains in part why the Protestant invented and proclaims a false "Gospel of Personal Salvation," rather than proclaiming the Gospel of the Kingdom of God.
(7) The Gospel of the Kingdom of God is directed exclusively to descendants of the line Abraham-Isaac-Jacob. Indeed, the term "nations" (Greek ETHNOS, which means "nation," "people," or "tribe") refers primarily to the descendants of the ten tribes of the Northern Kingdom of Israel, which were disenfranchised and scattered circa 721 B.C., and in the Scripture are termed "Gentiles."
(8) The Gospel includes instruction whereby those to whom it is addressed may enter the Way of Life and attain to citizenship in the Kingdom. It hardly needs to be said that the "missionary" who offers Salvation to men who are not of the line Abraham-Isaac-Jacob does so fraudulently, for his offer shall not be honoured by the Lord God.
As to the notion that the so-called "Great Tribulation" is the greatest calamity ever experienced in the history of the World, consider the Prophecy of Daniel:
Daniel 12:1 -- And at that time shall Michael stand up, the great prince which standeth for the children of thy people: and there shall be a time of trouble, SUCH AS NEVER WAS SINCE THERE WAS A NATION EVEN TO THAT SAME TIME: and at that time thy people shall be delivered, every one that shall be found written in the book.
Clearly, the "great tribulation" of which Jesus speaks in the Olivet Discourse refers only to the suffering and trials experienced by the nation of Israel in the A.D. 70 destruction of Jerusalem. And yet, the Scriptural accounts regarding the siege of 721 B.C. and the siege of 586 B.C. (see Kings, Chronicles, Jeremiah, Lamentations, and the Psalms), together with the writings of Josephus concerning the A.D. 70 destruction of Jerusalem, leave no doubt that the judgments which the Lord God has brought against Israel have few historical parallels.