Level
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.
The level of a Pokémon will also affect breeding. Trying to breed two Pokémon with a large difference in levels will not result in an egg.
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 signifigantly high already.