Fault advantage is a very obscure mechanic. Here's how it works.

Fault Line

There is an invisible line down the center of the stage called the "Fault Line". If both players are on either side of the fault line, the game is in "Neutral Fault" and nothing special happens.

If both players are on the same side of the fault line, then whoever is further away from the line gets "Fault Advantage". The player will Fault Advantage deals additional damage depending on their Core, and the player with Fault Disadvantage deals less damage.

If this mechanic is too confusing for you, just look at the broken heart at the top of the screen. If it's your color, then you're dealing additional damage.