Levels as a term can mean several different things, this is disambiguation between those:
Commander Level Edit
The commander level is the prospective level for the player themselves. You gain experience by batting in the Battle Arena and Plains. Every time you level up, you gain Commander Skill Points, ready to be implemented into new skills that can be unlocked. Also, you will gain access to better tier Mechs.
Mech Level Edit
Mechs have their own levels, and while they may roughly be the same as the player's commander level, they are unique to that mech. Just like with commander levels, mechs level up via battles at the Battle Arena and Plains, and they will gain Circuits and Wires (the latter up to about Level 50) to use.
Drazil Level Edit
Drazils in Drazil Wars have their own levels, levels are gained by investing minerals into research areas. Each of the four minerals can be used to train two stats. The Drazil level is the average of it's level in the 8 training areas.