This is the Western Wall, all that is left of Temple Mount and the Jerusalem Temple destroyed for the last time in 70 CE by the Roman overlords in retaliation for a failed revolt. It was called the Wailing Wall before 1967 because Israelis did not control the area after the 1948 settlement of the Israel Palestine conflict. The wailing descriptor represented their loss of not being able to pray at this holiest of sites.
The war in 1967 continued the unresolved conflict of 1946-48. In 1967, the Arab nations surrounding the state of Israel amassed together to settle the unfinished business and finally, in their words, push the Jews into the sea. Israel prevailed against enormous odds with precisely executed strategic warfare and in the process took control of all of Jerusalem and Temple Mount. It is no longer the Wailing Wall but the Western Wall. The last wailing was wailing of elation when the tough battle-hardened Israeli soldiers fighting their way through the old city, under constant gunfire, heavy fighting doorway to doorway , who coming onto the wall of Temple Mount, at its first sight, broke down in sobs of joy.
The wall, all that is left of the temple, has become the holy destination for Jewish prayer and ritual. The orthodox pray at the wall and some leave notes in the cracks between the stone blocks, petitions to their One Almighty Living God. Social workers go through at night collecting the notes and reading the transcripts look for any ways to help out the petitioners.