Jesus continued in Matthew 24:32-35:
"Now learn this parable from the fig tree: When its branch has already become tender and puts forth leaves, you know that summer is near. So you also, when you see all these things, know that it is near--at the doors! Assuredly, I say to you, this generation will by no means pass away till all these things take place. Heaven and earth will pass away, but My words will by no means pass away."
The object Jesus refers to in this illustration (a fig tree) is certainly appropriate since there were many fig trees on the Mount of Olives. "When its branch has already become tender and puts forth leaves, you know that summer is near" - This would have been common knowledge for those in Palestine. "So you also, when you see all these things, know that it is near--at the doors!" When the things that Jesus had been describing (in 24:4ff) started taking place, they would know that Jerusalem's destruction was exceedingly close. John the baptizer preached that the ax was laid at the root of the trees (cf. 3:10). Jesus here foretells that the ax would fall upon the impenitent Jewish nation within that generation.
Let it be noted that some have tried to get around the clear meaning of Matthew 24:34 by stating that the word "generation" could mean "race" or "nation." A careful look at how this word is used elsewhere by Matthew will disprove this notion (e.g., 1:17; 12:38-45).
"Heaven and earth will pass away, but My words will by no means pass away" - Certainly the disciples had difficulty believing all that Jesus had just foretold regarding the destruction of Jerusalem and the temple. Thus, Jesus assures them that His predictions (i.e., His "words") were even more certain and stable than Earth itself. Not even the heavens were as abiding in their permanence as His utterances; they would (and did) come to pass!