The Western Wall (formerly known as the Wailing Wall)

The Western Wall is that one big wall straight ahead.  It is what is left of the Temple.  The wide light colored area to the left is men only.  The small darker area is for the women.  There is a wall in between the two as well.  Mothers climb on chairs to peek over to see their Jewish sons' Bar Mitzvahed with groups of men on the other side - it is cute. People pray at the wall and tuck notes with prayers written on them into the cracks and crevices of the wall.

The whole area is called the "Temple Mount" and above and off to the left is the Dome of the Rock, which is a very holy place for Muslims.

Wikipedia: 
The Western Wall, Wailing Wall or Kotel is located in the Old City of Jerusalem. It is a relatively small western segment of the walls surrounding the area called the Temple Mount by Jews, Christians and most Western sources, and known to Muslims as the Noble Sanctuary
The Temple Mount is the holiest site in Judaism and is the place to which Jews turn during prayer. The original, natural and irregular-shaped Temple Mount was gradually extended to allow for an ever larger Temple compound to be built at its top. This process was finalised by Herod the Great, who created an enclosing, almost rectangular set of retaining walls, which supported extensive substructures and earth fills, then hidden under a vast paved platform. Of the four retaining walls, the western one is considered to be closest to the former Temple, which makes it the most sacred site recognized by Judaism outside the Temple Mount itself. Just over half the wall's total height, dates from the end of the Second Temple period, and is commonly believed to have been built around 19 BCE by Herod the Great, although recent excavations indicate that the work was not finished during Herod's lifetime. The term Western Wall with its variations is mostly used in a narrow sense for the section traditionally used by Jews for prayer and also known, mainly in the past, as the "Wailing Wall", but in a larger sense it refers to the entire 488 meter-long retaining wall on the western side of the Temple Mount. The classic portion now faces a large plaza in the Jewish Quarter, near the southwestern corner of the Temple Mount, while the rest of the wall is concealed behind structures in the Muslim Quarter, with the small exception of a 25 ft (8 m) section, the so-called Little Western Wall.
The wall has been a site for Jewish prayer and pilgrimage for centuries; the earliest source mentioning Jewish attachment to the site dates back to the 4th century.