It is key on a mountain bike. On a road bike, it is important to keep your pressure up for less rolling resistance and not quite as important for traction.
But for mountain biking, it is really important. It helps control how much you slip, how much you get bumped around, how your bike handles, etc. I usually put a little less tire pressure in my front tire than my rear, since my fat butt is sitting on the seat and there is usually more weight there to keep from flatting as much. I have run, even with regular tubed tires, as low as 25 when the conditions were just right. I was probably asking for a flat, but I took the risk. By the way, I did not flat!

