The Mishnah on today’s daf (=page) teaches the following in the name of Rabbi Shimon:
The law relating to blood is lenient at the beginning of the offering ceremony and stringent at the end, while that relating to libations is stringent at the beginning and lenient at the end. Blood is exempted from the law of sacrilege at the beginning, but is subject to it after it has flowed away to the Kidron wadi, while libations are subject to the law of sacrilege at the beginning, but are exempted from it after they flowed down into the shittin.
Regarding sacrificial blood, the Gemara in Massekhet Yoma (daf 58b) teaches that once the kohen gadol completed the sprinkling of the blood on the corners of the mizbe’ah, the Mishnah teaches that he sprinkled blood on the altar itself (see Vayikra 16:19) before pouring the remainder of the blood down a drain that was built into the foundation of the altar itself. This blood mixed in the plumbing pipes of the Temple with the remainder of other blood that had been poured into a similar drain in the outer altar. From there they emptied into the Kidron Valley, where their remains were sold as fertilizer.
From this topographical map, which includes, in its center, the Second Temple-era platform on which the mikdash stood, it is clear that the Kidron Valley, running to the east of the Temple Mount, is the natural run-off point for sewage from the Temple. The walls of the Temple Mount actually stand at the very edge of the banks of the dry river, in which the Shiloahspring flows.
The definition of shittin appears in Massekhet Sukkah (daf 49), which discusses the two bowls on the altar – sefalim – that drained into the foundation of the Temple. Rabbah bar bar Hannah quotes Rabbi Yohanan as interpreting a passage in Shir ha-Shirim (7:2) as teaching that these drains – shittin – existed from the time of creation.
The Rishonim and Aharonim point out that it is difficult to reconcile Rabbi Yohanan’s teaching that the shittin are part of God’s creation with a statement made by him later on in the Gemara that describes King David as having them dug. Many answers are given to this question – e.g. that they were closed up at some point and that King David reopened them, or that Rabbi Yohanan is presenting the opinions of two different Tanna’im. The Maharsha explains simply that the term shittin refers to different things. In our discussion they are the pipes through which the wine and water that are spilled on the altar drain down into the Kidron Valley; in the later statement the shittin (or shattot) are the foundation of the altar itself.