It is the remnants of the wall that surrounded the Second Temple.
The Western Wall is an important religious site to Jews. It is the only remnant of the Holy Temple - destroyed in 70AD. Jews gather to pray there several times every day and have been doing so since...
The Western Wall is the only remaining portion of the Second Temple's retaining wall which is at the base of the Temple Mount.
Some options are: Watch people, see what other visitors are doing, take pictures, pray.