On the first day of Rosh Hashana (or the 2nd day when the first day of Rosh Hashana is on Shabbos), following the afternoon prayer, we visit a body of water or pond containing live fish and recite the Tashlich prayers, in which we "cast away" our sins.

As fish depend upon water, so do we depend upon G-d's providence. Also, a fish's eyes never close, symbolizing G-d's unceasing watchfulness over us.