Each time your brute gains a level you may receive bonuses. This could be a Weapon or Special, or Attributes improvement. To gain levels you need experience. Each level-up requires more experience. The increase in requirement is not linear.
It takes more and more effort to level up at higher levels. Experience is very limited (only 3 fights are allowed daily so you can only get max 6 exp daily), so receiving pupils are the only ways to get more experience after that. Normally speaking, it can take several months of playing to surpass level 20. However there are a few players who cheat and get 100+ levels within.