I'm not really sure about the science behind why our eyes water so much and burn while cutting an onion. However, I have found that chewing gum while cutting an onion helps keep your eyes from burning. Not sure why, but it really helps me :)
I believe onions give off a gas which irritates the eyes, although I'm not sure what gas it is. The way I avoid the problem is by refrigerating the onion before I slice it. This doesn't eliminate the problem but it does mitigate it considerably.