Ghost Tag functions like the fighting game equivalent of lap-time ghosts in an online racing game. When a player fights someone online, their opponent's match configuration (characters, costume colors, gem setup, etc) is recorded and saved for later. The player can then go back and re-fight that specific match, albeit it against CPU-controlled characters rather than an actual person.
While in Ghost Tag mode, players can "Swap Switch" their team, taking control of the ghost characters saved earlier. While it does not appear as though they'll be able to be used in actual online fights, it may help you figure out how that Zangief player Atomic Buster'd you so hard your Vita disconnected from the Internet.