Why does chopping onions make you cry?

When you chop an onion, you break open some of the onion's cells. This releases enzymes which take part in complex biochemical reactions. 

One of these reactions on allicin (2-Propene-1-sulfinothioic acid S-2-propenyl ester, (C₆H₁₀OS₂) produces a substance called propenyl sulphuric acid. This is very volatile and also an irritant. It ‘fumes’ up from the onion and irritates your eyes, which produce tears to wash away the irritant and protect themselves.