“The Wall” you refer to is the westernmost retaining wall of the Temple Mount, and dates from the Second Temple era. In the late 19th and early 20th centuries the British began referring to it as the Wailing Wall, based on the old Arabic name for it, El Mabka, the place of weeping. Jews, however, have always referred to the wall as the Western Wall, preferring to relate it to the Holy Temple.
In Hebrew it is called Hakotel Hama’aravi (The Western Wall), or simply, the “Kotel”.
Tens of thousands of Jews from all over the world, representing every level of religiosity, learned or not, Zionist and non-Zionist, visit the Western Wall every year.
Many Jews who visit have no knowledge of the Temple at all; many know little or nothing about Judaism or Jewish history. And yet, the Western Wall draws them like a magnet and often elicits from them deep spiritual feelings. For many people, a single visit to the Western Wall has changed their lives by prompting them to investigate their Jewish roots. We believe that much of this remarkable energy is due to the fact that “the Divine Presence never left the Western Wall.”