Final Fantasy XII will indeed be using a system called License Board. Many things in this game require license, even the abilites. Abilities, weapons, magic, skills, (I think even summons) all need license to be used. Even if you have learned an ability or gained a weapon already, you can't use/equip them without a license. To earn a license, you need to gain enough license points (LP), which will be acquired along with EXP by defeating enemies.
Also, as SrBehemoth said, everyone could use a summon, but only one can be equipped at a time. Also, to gain a summon, you must beat them first. Then, the summon creature must sign a pact with the character who will equip them. My guess is that you can also change your equipped summon if you are tired with the one you currently have, and there might be more than six summons. (because it's not great if there are only six, the more the better)