The bergamot orange is believed to be a hybrid of the bitter orange and the lemon, resulting in a rather bitter fruit. It is rarely, if ever, eaten unadulterated, but is often used as a flavoring and a perfume.
The single best known use of bergamot is as a flavoring for tea, particularly Earl Grey and Lady Grey. It is also one of many bitter orange varieties used in making marmalade, although it is not the most common, and most producers will specify if a product is bergamot marmalade (bergamot jam is also available; I do not know what the difference is). It is used in flavoring in everything from Turkish delight to snus, and is used in many perfumes. It may also be used in place of lemon in many recipes. However, there are health concerns in eating large amounts, so use some common sense, and do not make bergamot-ade or bergamot pie.
Unfortunately, there has not been much good research of the ill-effects of eating too much bergamot. In larger doses it may cause muscle cramps, and it may interfere with the metabolism of some drugs; check with your doctor (you may need to tell them to look for drugs with grapefruit–drug interactions, rather than relying on their extensive knowledge of bergamot). It is also photocarcinogenic, although this is not an issue unless you are smearing it on your skin (as people did, in the 60s, when it was an ingredient in some sunscreens). Please do not use bergamot oil for any medicinal purposes; it's just not wise.