From Bulbapedia, the community-driven Pokémon encyclopedia.

Levels are used in all of the Pokémon RPGs as a measurement of how strong a Pokémon currently is. It is determined by how much experience that Pokémon has. A Pokémon's level will range from 1 to 100. When a Pokémon gains a level, its stats increase by a small amount. It may also learn a new move or evolve.

A Pokémon's level will also affect its happiness, raising it slightly when the Pokémon levels up. This means that a Pichu trained in battle will eventually evolve into a Pikachu, with its happiness going up slightly each level. However, this is not the case with using Rare Candies, and a Pokémon that evolves by tameness will usually not evolve through their use, unless, of course, its tameness rating is significantly high already.

Also, when a Pokémon has reached level 100 it cannot continue gaining Effort Points in Generation IV. In games before Generation III, however, the player can use the box trick.