Tournaments let you increase your brute's ranking. When you are eliminated from a tournament you gain 1 xp for each round you won. So if you lose in the first round you gain 0 xp, but if you lose in round two you gain 1 xp.
If you manage to win the tournament your brute's ranking increases. The downside to that is everything else about your brute is reset and it returns to level 1. The good news is that you are now given the choice to either use the same destiny (i.e. get the same choices as you were given last time, either making your brute the same or fixing bad choices you made) or pick a new destiny (so you get new random choices each time you level up, so your brute could be better, or maybe worse, than it was before). (July 28 2015) Search for Brix Anthony Batulan in Facebook for he will be aiding you some workarounds with the new My Brute powered by Muxxu.