Level

Levels are the general competency of the player character in the SPECIAL character system. A measure of your experience and abilities. Your Level is determined by the Experience Points you have earned throughout your journey.

Each time you Level up, you can modify your Skills but not your Primary Statistics. You can also gain special perks depending on your character. Therefore you become stronger and better with each Level you gain.

Level cap
The maximum level you can reach varies from game to game. In the first Fallout it's 21, in Fallout 2 it's 99, while in Fallout 3 it's 20 (30 with Broken Steel add-on).