Question posed by Bella.
Comets are known in some circles as 'dirty snowballs'. This is not because they are made of snow and/or have questionable hygiene, but is an affectionate term that hints at their composition.
The 'snowball' bit comes from the fact that comets are thought to consist of varying but significant quantities of ice. Specifically, this means water ice, which is the stuff you're familiar with from plonking it in your Pimm's on a hot day. Along with this water ice is a variety of frozen gases such as methane, ammonia, carbon monoxide and carbon dioxide.
The 'dirty' bit comes from all the other stuff that's mixed up in there too: first up is a load of rock and dust, but also included are some organic compounds including methanol, ethanol and hydrogen cyanide (among others). It has also been suggested (with some sensible thought and a little bit of evidence behind it) that some more complex long-chain hydrocarbons and amino acids may be found on some comets. In fact, it has been postulated that cometary impacts with Earth may have been what deposited these essential (for life) compounds on our planet in the first place.
When a comet passes close enough to the Sun the frozen gases thaw and form a relatively large but thin atmosphere around the comet (the 'coma' and tail), leaving behind the organic compounds and rocks (the 'nucleus' of the comet). These organic compounds make a dark mixture (much like crude oil) which means that, contrary to the image brought to mind by the term 'dirty snowball', they're not very white (other than when they're outgassing near the sun, looking pretty awesome). In fact, when they're far away from the Sun's heat and therefore dormant, they're among the darkest objects in our solar system, many reflecting less light than asphalt does. This makes them pretty difficult to find!
Here's a great video that does an exceptional job of demonstrating what comets are made of:
Possibly the most famous comet is Halley's, which appears in the inner solar system every 75 to 76 years (the next visit is planned for 2061; get the tea & crumpets ready.) The only comet I've ever seen is Hale-Bopp, which was visible for a whopping 18 months back in 1997. Others you may have heard of include Shoemaker-Levy 9 which, whilst not visible to the naked eye here on Earth, created something of a media storm in 1994 by crashing into Jupiter; comet Lovejoy, which miraculously survived a close encounter with the Sun* in December of last year (2011); and comet Swan, which didn't survive its encounter with our star in March of this year (2012).
* I'm not sure if it sold any dodgy antiques while it was there.
read more: What Are Comets Made Of?