Level is a personal characteristic, indicating how advanced the Trooper is in terms of combat ability. Unlike most games featuring specialisations and customisations, levelling in MiniTroopers is achieved by earning Credits. They are rewarded for various actions you can do every day from the Headquarters. Note that your troopers' individual performance and kills won't affect their levelling capabilities; victory is all that matters in this regard.
The point of increasing your troopers' levels is to gain new Skills, whose effects vary, but cover all of the troopers' actions. The costs for levelling up increase progressively. On the bright side, however, within the first few levels, your troopers are granted additional options to customize their combat behaviour.
For costs and other details, please see the links provided.