It's what could happen. Francois Rabelais is referring to death. Living people are always thinking about what might happen after death so there are a lot of "Perhaps .... (insert idea about death here)" but in Looking for Alaska, Pudge's Great Perhaps is what he could do and experience in life. It's not a defined goal, it's the possibility of adventure, of what could be.
I am not really sure but I always presumed that its referring to life. Although our own 'worlds' or lives revolve around ourselves, in reality we barely count. I think the great perhaps is whatever is going to make us matter, really exist, in the whole scheme of things. Expanding on this, not everyone will achieve/find/something the Great Perhaps... thats why it is a Perhaps. Like Leah said, its like an adventure that will happen for some and not for others.
I dont really know if its right, its just what I think