Chemistry of an Onion

The answer is really attributable to several different series of reactions:

1. The various sulfur compounds react with one another and other compounds to form new and interesting flavor compounds
2. If you let the onions brown the the natural sugars in the onion start to brown and carmelize.
3. Beyond carmelizing there is the Maillard reaction. This is another form of non-enzymatic browning which is the product of sugars and amino acids
   

References:
On Food and Cooking by Harold McGee:

The relevant pages on Onions, 311-312: Google Print link.
Pages on browning reactions, 779: Google Print Link.

Molecular Gastronomy by Hervé This, Malcolm DeBevoise (Translator)