Paper Princess is correct.
Another way I describe it to people is think about the track at your local high school. The outer lane is longer than the inner lane, right? So now think of your binding as a track. As the fabric curves from the top to the bottom, you have 2 layers of binding going around the raw edge of the quilt - you have an inner lane and an outer lane. If you don't press it, the fabric is free to adjust itself and make the inner lane shorter and the outer lane longer, and the binding will lay nice and flat. If you press it, the inner lane is forced to stay where it's at, and it bunches up in its "lane" (the inside layer of binding).
Try it out - make placemats or mug rugs, do one pressed and one unpressed, see which one you like better. It seems like such a small, unimportant thing, but it really does make a difference.