One day the disciples asked Jesus when He would return, and what signs they should be looking for just before He would return. Like most of us, they were positive that they were living during the last days of man's rule and that Jesus was going to set up His kingdom during their lives. They were wrong. Many Christians have also been wrong since. What Jesus told them was the first sign, did occur in their lifetime, leading them to believe even more that they were living during the end times. He said, “Do you see all these buildings? Truly I say to you, they will be so completely demolished that not one stone will be left on top of another!”

Within 40 years, this happened. On the 10th of August, in A.D. 70 -- the 9th of Av -- in Jewish reckoning, the very day when the King of Babylon burned the Temple in 586 B.C., the Temple was burned again. Titus took the city and put it to the torch, burning the Temple. Jewish historian, Flavius Josephus was present in Jerusalem when the city was captured and the Temple was burnt. He described the event in this manner:

The Romans, though it was a terrible struggle to collect the timber, raised their platforms in twenty-one days, having as described before stripped the whole area in a circle round the town to a distance of ten miles. The countryside like the City was a pitiful sight; for where once there had been a lovely vista of woods and parks there was nothing but desert and stumps of trees. No one - not even a foreigner - who had seen the Old Judea and the glorious suburbs of the City, and now set eyes on her present desolation, could have helped sighing and groaning at so terrible a change; for every trace of beauty had been blotted out by war, and nobody who had known it in the past and came upon it suddenly would have recognized the place: when he was already there he would still have been looking for the City. (Ref. 3)

Josephus speaks of the house to house fighting that occurred:

These Romans put the Jews to flight, and proceeded as far as the holy house itself. At which time one of the soldiers, without staying for any orders, and without any concern or dread upon him at so great an undertaking, and being hurried on by a certain divine fury, snatched some what out of the materials that were on fire, and being lifted up by another soldier, he set fire to a golden window, through which there was a passage to the rooms that were round about the holy house, on the north side of it. As the flames went upward, the Jews made a great clamor, such as so mighty an affliction required, and ran together to prevent it; and now they spared not their lives any longer, nor suffered anything to restrain their force, since that holy house was perishing . . . thus it was the holy house burnt down . . . Nor can one imagine any thing greater or more terrible than this noise; for there was at once a shout of the Roman Legions, who were marching all together, and a sad clamor of the seditious, who were now surrounded with fire and sword . . . the people under a great consternation, made sad moans at the calamity they were under . . . Yet was the misery itself more terrible than this disorder; for one would have thought that the hill itself, on which the Temple stood, was seething hot, as full of fire on every part of it. (Ref. 4)

And Josephus lists the horrendous outcome:

To give a detailed account of their outrageous conduct is impossible, but we may sum it up by saying that no other city has ever endured such horrors, and no generation in history has fathered such wickedness. In the end they brought the whole Hebrew race into contempt in order to make their own impiety seem less outrageous in foreign eyes, and confessed the painful truth that they were slaves, the dregs of humanity, bastards, and outcasts of their nation.

....It is certain that when from the upper city they watched the Temple burning they did not turn a hair, though many Romans were moved to tears. (Ref. 5)

The prediction of Jesus with regard to the city and the Temple were now almost fulfilled:

As the flames shot into the air the Jews sent up a cry that matched the calamity and dashed to the rescue, with no thought now of saving their lives or husbanding their strength; for that which hitherto they had guarded so devotedly was disappearing before their eyes. (Ref. 6)

Jerusalem was totally destroyed but not as Jesus had predicted - "not one stone was left upon another."  The Plain Truth is that the wall of the Temple (now called the 'wailing wall') is still with us. When the Temple was set on fire the Roman soldiers tore apart the stone to get the melted gold. The Menorah and vessels were carried to Rome and the treasury was robbed. So another destruction of that wall is yet to come.

As Daniel had predicted the Temple was destroyed after the Messiah had come, not before.

Bible scholar Ray C. Stedman comments on the predictions of Jesus and their fulfillment in history a few years later,

In Luke 21:20 we have other details of this predicted overthrow of the city and the Temple. There Jesus adds, "But when you see Jerusalem surrounded by armies, then know that its desolation has come near." Forty years later the Roman armies under Titus came in and fulfilled the prediction to the very letter. With Titus was a Jewish historian named Josephus who recorded the terrible story in minute detail. It was one of the most ghastly sieges in all history. When the Romans came the city was divided among three warring factions of Jews who were so at each others' throats that they paid no heed to the approach of the Romans. Thus Titus came up and surrounded the city while it was distracted by its own internecine warfare. The Romans assaulted the walls again and again, and gave every opportunity to the Jews to surrender and save their capital from destruction.

Quotes and drawings from from http://www.templemount.org/destruct2.html