If you suppose you love your girlfriend, you may not be too sure. Suppose means to guess, or think, or imagine something without absolute certainty. Best hold off on the engagement ring until you know for sure!
Suppose also has the meaning of assuming something hypothetical for the sake of argument. You might ask, "Suppose someone breaks in while I'm away?" Suppose also has the more technical (and often legal) sense of something you must take for granted if some other condition is to happen. Your theory might suppose the victim was home by 8:00. In this last sense, suppose introduces something that's a precondition.