Joseph Telushkin, rabbi and author, in his 1991 book Jewish Literacy, wrote the following:
"When Rome destroyed the Second Temple in 70 C.E., only one outer wall remained standing. The Romans probably would have destroyed that wall as well, but it must have seemed too insignificant to them; it was not even part of the Temple itself, just an outer wall surrounding the Temple Mount. For the Jews, however, this remnant of what was the most sacred building in the Jewish world quickly became the holiest spot in Jewish life.
Throughout the centuries Jews from throughout the world made the difficult pilgrimage to Palestine, and immediately headed for the Kotel ha-Ma'aravi (the Western Wall) to thank God. The prayers offered at the Kotel were so heartfelt that gentiles began calling the site the 'Wailing Wall.' This undignified name never won a wide following among traditional Jews; the term 'Wailing Wall' is not used in Hebrew."