Atlus has given a bit of detail on the Social Links in
Persona 4 Golden. Now granted I've never played a Persona game before (yeah, I need to rectify that at some point) so I'm not sure if social links have been present in past games before, but I honestly thought it was referring to a way to connect Facebook or Twitter to the game somehow. Anyway, the Social Link system will allow you to connect with the characters as non-superficially as the game is capable of, letting you choose whom you spend your time with and strengthening relationships that will help you in battle. Some of your decisions can affect your own character by way of status upgrades as well.
Persona 4 Golden is currently set to launch November 20th on the PS Vita.