Griever does not exist in the "real" world of Final Fantasy VIII until he is summoned by Ultimecia. It is a symbol of Squall, he is the creator of the idea of what that lion-demon-whatever is. Ultimecia can read minds and partially control reality. That is why she was able to summon him. It is not explained in the Ultimania how much of reality she can control and "create" things this way but at least she can do that. That is pretty powerful, actually.