Vegans remove all products that involve animals (including insects) -- for example milk and eggs -- from their lives, usually for ethical and environmental reasons.
There is a bit of variety in the vegan community; Europeans and Americans not only pronounce it differently, European vegans also generally won't eat honey, while American ones generally will. Some vegans won't drink beers and wines clarified with bonemeal (even though the bone meal is not present in the final product), others will. Veganism can be taken to the extreme; some vegans won't eat food cooked in pans if they have ever been used to cook meat, other vegans are content to simply remove meat, fish, eggs, & milk from their diets.
Most people calling themselves "vegetarians" today do not mean that they are vegans... they mean that they are "ovo lacto vegetarians", who eat milk and eggs.
See also Vegetarianism