Square Enix updated the Bravely Default official site with details on the "friend summon" feature that was revealed in Jump last week.
Friend Summon is one of the commands on your battle palette, which also includes fight, ability, brave, default and flee. Access this command, and you can summon a friend's character into battle to perform a particular move. You get these friend summons through two means: local and internet data transfer with friends, and StreetPass.
To send out a summon to other players, you first select "send" from the Friend Summon command menu. You then select the move you want associated with the summon -- this is the move that your character will perform when another player calls him out into battle. The summon is sent out to all your friends, and to strangers via StreetPass.
Friend summons that you've gathered can be made stronger. By using a particular friend summon multiple times, you can raise its "affection" parameter, which increases the summon's strength.