The Western Wall is a place of pilgrimage for Jews from all over the world. It is the one remaining wall from Herod's Temple Mount. Throughout nearly two thousand years in exile Jews all over the world turned towards the wall to pray for a return to their land.
The 'Wailing wall' was so called because during the Jordanian occupation of Jerusalem (1948-1967), Jews could not get there.
Jews often write prayers on little slips of paper and put those into the crevasses in the wall. They go and pray at the wall, and yes, they do wail. People who have visited say that it is an incredible sound, very mournful and very moving.
Quite recently the wall was split into two sections, an area for the men to go and pray, and an area for the ladies to go and pray. Ladies are not allowed in the men's area, families cannot be together at this very holy place.
