In the game of pool (or billiards), to oversimplfy a lot, your goal is to knock billiard balls into the pockets -- holes arranged around the edge of the pool table. (note that the meaning of the word "pool" as used here has nothing to do with water)
One rule people sometimes use is that you have to "call your shots" -- you have to state which of the balls you intend to sink and into which pocket.
A stereotypical format for doing so is "nine ball, corner pocket", with a gesture to indicate which corner of the table you mean. Pool balls are numbered 1 through 15, so this means you intend to sink ball #9 in the indicated pocket in the corner of the table. (there are also "side pockets")
In media, you often hear this with the nine ball or the eight ball specifically, since those balls are related to the victory conditions in some versions of the game. Also, "nine ball" flows off the tongue well.