In the
Playstation RPG Final Fantasy VIII, a Guardian Force (GF) is a
character that can be
junctioned to a player character to give him special powers, including the ability to use
magic in combat. Guardian Force characters have
HP and
experience like normal characters, and can be
summoned to shield the player character with its life force and unleash a
can of whoopass on your opponent. While they can not actually die, a Guardian Force character without hit points can not be summoned. Developing your PCs' relationship with Guardian Force characters, and discovering more about the effect junctioning with them has on your character, is a fundamental part of playing FFVIII.
GF Management is complicated because GF's watch your movements and actions in combat to a certain degree, and become more or less compatible with you. For example, Shiva will like you more if you use Ice spells, but Ifrit will dislike you for it. Brothers might be indifferent. Your compatibility rating determines how long it takes to summon your GF, but has no other effect AFAIK.