Why do onions make your eyes water?

In normal circumstances, our lovely eyes are always being watered by up to 1/4 of a teaspoon per day of the secretions to keep our eyes moist and to wash away dirt or foreign particles and bacteria. These fluid secretions are drained away by tear ducts. When tears are secreted faster than they can be drained, the excess tears flow out of the eyes and run down the face. This is observed when we cry.

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When peeling or cutting an onion, it makes eyes water because of the sulfur-rich oil being released from the onion. This oil readily evaporates in the air and soon it reaches the eyes. The nerve endings in the conjunctiva ( this is the transparent tissue that covers the eyes and underside of eyelids) gets irritated by this sulfurous oil from the onion. The instinctive reaction then is for the sensitized nerve to send signals which stimulates the tear ( lacrimal ) gland in both eyes to produce extra fluid. This extra fluid which is the tears then wash over the eyes to flush out the irritating substance from the onion.
Putting the onions under water while cutting them will help reduce tears because the water will capture most of the juices of the sulfur-rich oil.

Reference: Reader's Digest Why In The World