To begin with, I should explain what "Garden" is.
Garden is a strange shaped academy which serves to train young people ages 6-19 to become soldiers, as well as to use magic, a feat that no other people in the world of Final Fantasy VIII can accomplish. If the student does not pass the graduation exam between the ages of 15 and 19, they are expelled from Garden.
The more exceptional students of Garden may graduate to become a member of SeeD, Garden's special forces.

The world appears to be peaceful, although it actually stands in a precarious position in which one small turn can plunge it into war. Garden was created in this world, a private school of soldiers to help settle disputes to keep them from getting out of hand, located at three positions around the world, independant from any country, destroying the seeds of war and keeping military forces in balance. But it was no longer peaceful, once the witch awoke.

At the very beginning of the game, Squall Leonhart is a SeeD trainee trying very hard to graduate, a skilled fighter with his gunblade (a strange cross between a gun and sword). Later on, at a party for new recruits, he meets a woman named Rinoa although they do not actually learn who each other is until a bit later in the game when he meets her again in a forest and learns that she's the leader of a group of rebels known as "Forest Owls", who fight against the Galbadia army. The Forest Owls are not very affective against Galbadia and seem to have little concern for the consequences of their actions.
After meeting Rinoa, Squall dreams that he is a man named Laguna Loire, and is on a mission with Kiros Seagill and Ward Zabac.

Under the influence of Edea the witch, Galbadia declares war on the rest of the world, and so Squall is sent on a mission to assassinate her. But Edea has Seifer, Squall's rival (Seifer hates Squall for making it into SeeD while he himself didn't due to his temper) with his two assistants, Raijin and Fuujin. For more information on Edea or other characters, see the list to the left.

I don't want to give any more away...this is just a basic description, more about the world of Final Fantasy VIII and it's condition - if you want to experience the suspenseful adventure of the game, play it! I won't spoil it.