The label vinegar derives from the French vin aigre , "sour wine", which gives you the correct idea that it is a conversion of a fermented liquid like wine, beer or cider. Bacterial activity makes it into a weak solution of acetic acid, which is what makes vinegar sour. Vinegar is an ancient ingredient that has been used for centuries, not surprising given that the process of souring will occur naturally.
There are many kinds of vinegar available, many of which have been noded here on everything. Let me mention in particular one that hasn't: distilled white vinegar, made from grain alcohol. It was the only vinegar I knew growing up, and it's very harsh tasting, not the best choice for adding to foods. My mother used to use it to rinse my hair when I was a girl; it made my hair squeak when combed and didn't remove tangles, so I used to cry when she pulled that comb through. I hated it, and advise you to use a conditioner instead. However, white vinegar does makes a good environmentally friendly cleaner which cuts grease and grime well; just mix it with a little water and use it to clean household surfaces and windows. If they're really dirty, use a soapy cleaner first, then the vinegar solution after as a kind of rinse. You can also pour a little baking soda down a slow drain, followed by vinegar, to remove the clogs; this fizzes most excitingly.
Of the more palatable vinegars, I should extol malt vinegar, made from malted barley; it's mild in flavour and is often sprinkled on fish and chips in Britain and Canada. I miss malt vinegar when I have chips (French fries) in the States. Apple cider vinegar, well-described by mrklaw, has a fruity flavour and is thought to have medicinal properties. Glorious Italian balsamic vinegar, elixir of the gods, has been noded most ably by sneff, and I have written on the lovely mild rice vinegar. Vinaigrettes, dressings made from oil and vinegar, often use wine or fruit vinegars, usually made from berries.
See also sensei's How many ways can you say "vinegar"? for an alphabetical listing of types.
Vinegar should be kept in a cool, dark location. Once it has been opened, bacteria may cause it to become cloudy, and though this doesn't affect the taste, it does not look very nice.