For hundreds of years, after the destruction of the Temple, the Western Wall was not a prayer place for Jews living in the country. It was only in the 16th century, when the government began prohibiting Jews from ascending to the Temple Mount, that the Western Wall became a place of Jewish prayer and a symbol of yearning for the Temple. At the foot of the Western Wall there was a narrow alleyway where the Jews prayed as close as possible to the site of the Temple.
After the establishment of the State of Israel, when Jerusalem was divided (1948-1967), the Kingdom of Jordan ruled the Western Wall and prohibited Jewish access to the Wall. Many Jews used to go to Mount Zion and pray on King David's tomb, watching from the top of the building toward the Temple Mount and hoping for a day when they could go back and pray at the Western Wall.
At the end of the Six Day War, the worshipers streamed en masse to the Jewish Quarter and the Western Wall. Then houses of the Mughrabi neighborhood, which were adjacent to the Western Wall, were demolished and the large prayer plaza adjacent to the Western Wall was built.
The wall was built of hewn stones, huge in size, each weighing between 2 and 5 tons. Each of the stones of the Western Wall is carved in the manner typical of the construction of Herod's reign, with its slightly protruding stone center, as opposed to the carved stone frame, smoother and more submerged.
If you stand near the wall and look up, you will see that each layer of stones is retreated in about three centimeters, compared to the layer below. This is a construction technique whose function is to provide stability and strength to the ancient structure, since the construction of the massive structures and retaining walls at the time did not yet use concrete.
Today the Western Wall is used for religious services and gatherings, and many come to celebrate the Bar Mitzvah ceremony, completion of a military tracks, and other celebrations.
The religious answer was that it was the wall closest to the resting place of the Divine Presence. The Ark of the Covenant in the First Temple near the Western Wall. This was the case in the First Temple. But in the Second Temple the Ark of the Covenant was no longer in the Temple, so what saved the Wall from destruction?
The claim of the believers is that even if the Holy Ark has disappeared, the Divine Presence never moved from the Western Wall of the Temple and therefore it continued to preserved from destruction.
But there is another story, a Jewish legend, which explains the preservation of the Western Wall from destruction. According to the story, Titus, the commander of the Roman Legion who conquered Jerusalem, ordered four of the senior commanders under him to destroy the Jewish Temple. Each of them was ordered to demolish one of the walls of the Temple. The one who was left to destroy the Western Wall tried to carry out the order, but failed. When Titus asked him why he had not completed his ordered, the frightened commander replied that if he had destroyed the last remaining wall, future generations could not see how impressive the Temple was, before it was destroyed by Titus. Titus, pleased with the flattering answer, left the wall standing.
By the way, we know today that the Western Wall was much taller in height. Over the generations, the wall was almost completely destroyed and what remains of it is the Western Wall of today.