It's a volatile gas that the onion releases when it is sliced.

The onion itself contains an oil that contains the chemical element sulfur. Cutting an onion causes enzymes to mix with the sulfur compounds in the onion. This reaction gives off a volatile sulfur gas. When this gas reaches your eyes and reacts with the water that keeps them moist, it produces sulfuric acid. This is the same acid found in car batteries. Your first instinct is probably to rub your eyes, but this will actually make the irritation a lot worse. Because more than likely you have onion juice all over your fingers.

Ever noticed you don't cry as much when you slice a Vidalia Onion? This is due to the low sulfur content found in a Vidalia Onion. The soil used to grow a Vidalia Onion must be low in sulfur. This contributes to its sweet taste. Low sulfur in the soil means low sulfur content in the onion. This means less of the volatile sulfur gas that makes you cry.