(Shekalim 21a was studied on Friday, November 8, 2013 / 5 Kislev 5774.)
From the Koren Talmud Bavli (Steinsaltz translation, pp. 191, 195; literal translation in bold):
The mishna discusses the ritual purity of items found either in the Temple or in Jerusalem and its environs...All the vessels that are found in Jerusalem on the way down into the bathhouse, wherein one purifies vessels in a ritual bath, are ritually impure, and those found on the way up are ritually pure. The mishna explains: Their descent into the bathhouse is not by the same route as their ascent out of it, and it can be assumed that those found on the way down have not yet been immersed, while those found on the way up have been. This is the statement of Rabbi Meir.
At the southern end of the Temple Mount's Western Wall (Kotel) in Jerusalem's Old City, as well as in the area of the Southern Wall, there were many ritual baths (mikva'ot, sing. mikveh) found. They were dug here for the use of the tremendous numbers of Jewish pilgrims who would come to Jerusalem to sacrifice at the Temple, in particular during the Three Pilgrimage Festivals: Passover (Pesach), the Feast of Weeks / Pentecost (Shavuot), and Feast of Booths (Sukkot). One needed to be ritually pure before he entered the Temple precincts, in order to offer any sacrifices.
Below: A typical mikveh, from the water, looking up towards the entrance.
Below: From the area of the mikveh towards Robinson's Arch (protruding stones in the middle), above which would have been an entry to the Temple courtyard.