Guardian Forces are equipped to a specific character and they give that character a range of abilities and junctions according to which abilities that Guardian Force has learned. Guardian Forces are the "summons" in Final Fantasy 8 and are similar to the Summon Materia found in Final Fantasy 7.
Once you receive each Guardian Force you should ensure that you focus on having it learn its most useful abilites which are outlined in each of the GF profiles below. You can go to Cactuar Island in order to learn Guardian Force abilities much faster.
Click on a Guardian Force picture below to move to that section: