Brawl allows you to become a Dragon Trainer and control 3 Dragons during a Brawl against another Dragon Trainer. It is a 3 vs 3 turn based PVP combat feature where you need to fight, earn tokens and increase your ranking. 
To start a brawl, you must have at least 3 Dragons on Berk. In the brawl, your three dragons fight against an opponent. Chose your strike and swipe towards the dragon you wish to attack. 
The red bar on your opponents health will indicate the damage. 
The white circle surrounding the rank of the dragon, indicates who has the next turn.