Simply put, vegetarianism is the belief that eating meat is a rather unpleasant activity, particularly for the meat being eaten, and thus should be avoided if at all possible. Vegetarians give many reasons for this. Some say it's more healthy than eating meat, and point to numerous studies backing this claim. Others argue for the environmental reasons, pointing out that there's something just a little batty and indirect about growing fields of vegetables, feeding them to a cow, and then killing and eating the cow. Still others make ethical claims: to paraphrase Mr Rogers1, '...it probably had something to do with not eating something that once had a face.' A fair number of them are simply masochists with martyr complexes.
Generally, a vegetarian will not eat any type of animal meat at all, but will eat eggs and dairy products. Some people call themselves vegetarians but will eat fish. Some will eat chicken. A few will eat all kinds of meat and just feel really guilty about it afterwards. In the other extreme, some vegetarians (called vegans) shun all animal products including honey, although undertaking a Marxist critique of a beehive might be considered to be pushing it.
There have been many famous vegetarians in history including Albert Einstein, kd lang, Adolf Hitler, George Bernard Shaw, Martina Navratilova, Charlotte Brontë, Plato, and Ahmet Zappa. This list is probably a bit more eclectic than most vegetarians would care to admit.