Fishing rods are used to fish. The more you use a rod, the higher your fishing skill becomes. Only some squares of water contains fish at any given time, and once a fish is caught from a square, it will take around 30 minutes for it to respawn. Fishing is the only skill that is not related to combat.
As of the August 2005 Update, you will also need worms in order to catch fish. It is also a quite good lootbag item.