When you cut into an onion, a powerful acid sprays up into the air. If your eyes are in the way of the spray (which is likely if you are cutting onions), the acid, while not damaging to your skin, will cause your eyes to sting. Immediately, your lacrimal glands or tear glands, go into overdrive. Your eyes start to tear, and tears continue in excess until they've successfully gotten rid of the irritation. Cool, huh?