They're two types of crashes.
Say you're going around a corner leaned over. It's the side of the bike you fall to.
So a low side is where you wash out the tires and the bike slides away from you. You just fall over from the lean and slide along the ground. Not too serious of a fall, normally... if you're wearing leathers.
A HIGH side is where the bike loses traction for an instant, starts to slide and build up a little momentum in the direction of the slide, and then the tires suddenly regain traction. This causes a violent jerk of the bike AWAY from the corner, and the rider is thrown in the air over the top of the bike.
A high side is normally MUCH more serious, as you hit the ground from higher and tumble. MUCH more risk of broken bones and torn shoulders/ankles, etc.
I'll also point out that it doesn't need to be during a corner, but that's when they generally happen.
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