Youthful Brewmaster is mainly used to get a second battlecry from a minion. If the card has charge, it is also possible to attack with it, use Youthful Brewmaster's battlecry to return it to your hand, and play the minion again to attack a second time.
Another use for Youthful Brewmaster is to indirectly heal your minions. When a minion is returned to your hand, its stats reset, meaning that any damage it has suffered will be removed. This effect goes both ways, though, as any buffs you may have given to the minion will also disappear. Transformations, however, will not be reversed. If you return a unit that has been targeted by Polymorph or Hex, you will get a Sheep or Frog in your hand.