The knife is a fairly cheap tool to make, only requiring 1 metal and 1 haft. Knives can be made in all materials including stone.
Right clicking a piece of wood with a knife will "carve it" and give it the welded property such as a cactus. This allows the player to get to difficult-to-reach spot such as the mithril spots on the Mainland, the Arches, or the Lone Mountain. Knives can also be used as a substitute as a sword. However, the sword deals much more damage than the knife does, so you shouldn't take on a player with a sword using a knife.