Brawling will become available once you have brought elbow, knee, and kick at 86% each. The skill itself can then be practiced at a guildmaster, and will go up by using the same three abilities you used to get it.
It will offer a slight damage increase to regular hand to hand attacks, a noticeable damage increase to elbow, knee, and especially kick, and also grants minor defensive perks against those three melee skills when an opponent tries to use them on you. Whether that defensive perk comes in the form of higher avoidance, damage reduction, or both, I'm uncertain.
The passive damage increase to hand to hand attacks is the main attraction. As a hand to hand specialist, unarmed assassin, or predator stance ranger, you'll definitely want to get it. It's also at its best with a felar, as this minor damage increase brawling offers will stack with a felar's average 31 claw damage at hero.
In short, always get and perfect brawling if you're a felar melee class. And with another race it's probably still worth getting too.