Brave Trials are exactly what they sound like. You are able to pick up to 18 heroes from your own list and are pitted against players of similar ranking and power levels from the arena. All health points are recorded regardless of whether you win or lose (both yours and enemies) until you have no more heroes to play or if you opt out.
The prizes and amount of levels vary everyday as better prizes usually means more levels to fight. As you move on in the levels, your enemies get harder. Prizes include level 1/2 jade, gold, gems, etc.