This is where many of the prayers for forgiveness are recited. The most powerful of these is the Un'taneh Tokef , which tells of God's judgment. Jews don't believe that God is cruel or vengeful, but rather, that he seeks repentance. Shabbat-people recite the tashlich prayer near a body of water that contains living fish. This is an opportunity to figuratively cast away any final sins.
Some people use bits of bread to symbolically cast away their sins after reciting the prayer.
Water purifies, and the hope is that the sins won't be brought to the surface. The fish, with their eyes forever open, symbolize God's constant watching of us, and that they don't gossip. The second day of Rosh Hashanah is much like the first. Candle lighting, services, and meals all ensue. Pomegranates are often used for this.