The Western Wall is one of the most holy places in Judaism. It is a remnant of Herod's Temple (or more specifically the Temple Mount) dating from the destruction of Jerusalem during the First Jewish-Roman War, in 70 AD. It is also referred to as the Wailing Wall for the anguish that the Jews felt at the destruction of the temple. In the absence of a temple, Jewish sacrificial worship could not continue and the religion slowly evolved into the primarily Rabbinic form it exists in today. Though remnants of other walls of the Temple Mount exist, the western one holds particular importance because it is the closest to the location of the Holiest of Holies, the temple's inner sanctum where God was said to live. The Islamic Dome of the Rock currently sits on the previous site of the Holiest of Holies. Until very recently Jews were forbidden from entering the Dome of the Rock, thus the Western Wall was as close as they could get; Jews can now visit the Dome of the Rock on certain days, but many religious Jews will not because it is forbidden of anyone who is not a high priest to enter the Holiest of Holies. There is one particular spot inside the wall accessible by certain tunnels that some Ultra-Orthodox Jews pray at because it is almost under the Dome of the Rock.
When visiting the Western Wall, it is now a popular custom to write down some kind of wish or desire on a slip of paper and wedge it into a crack in the wall. The visiting area is segregated by gender because it is still used as a site of Orthodox Jewish worship, though it's a popular tourist spot nonetheless. Tours are offered of the archaeological excavation of that area of the Temple Mount.