As shown on page 8 there are several ways you can use your Advantages. The whole purpose of this is to give the player some flexible options. That way the same action doesn’t have to yield the same outcome every way. It’s more than just roll to attack and then roll for damage. In fact Advantages, themselves do not do damage.
In a social situation, an Advantage could become earning an onlooker’s trust. Someone who you didn’t know was there, but they were watching. It can be the jump, twist, and roll that gets you in position to do that COOL thing.
It’s everything but direct damage in itself. However, there are several moves that use Advantages to fuel them. Depending on the situation that may be the better move to make, especially if you’re trying to finish an opponent with a combo.