From The Vegan Society (1978*):
The word "veganism" denotes a philosophy and way of living which seeks to exclude — as far as is possible and practical — all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of humans, animals and the environment.
What's the difference between being a vegan and eating vegan?
• A person who agrees in - and practices - veganism is called a vegan.
• A person who doesn't necesarrily agree with the part about animal exploitation, but live on a plant based diet, would probably say "I eat vegan" instead of "I am a vegan".

Regarding the health aspect of living on a vegan diet - which should be interesting both both for vegans and 'vegan fooders', here's what ADA, the world's largest organization of dieticians say:

It is the position of the American Dietetic Association that appropriately planned vegetarian diets, including total vegetarian or vegan diets, are healthful, nutritionally adequate, and may provide health benefits in the prevention and treatment of certain diseases. Well-planned vegetarian diets are appropriate for individuals during all stages of the life cycle, including pregnancy, lactation, infancy, childhood, and adolescence, and for athletes. A vegetarian diet is defined as one that does not include meat (including fowl) or seafood, or products containing those foods. This article reviews the current data related to key nutrients for vegetarians including protein, n-3 fatty acids, iron, zinc, iodine, calcium, and vitamins D and B-12. A vegetarian diet can meet current recommendations for all of these nutrients. In some cases, supplements or fortified foods can provide useful amounts of important nutrients. An evidence-based review showed that vegetarian diets can be nutritionally adequate in pregnancy and result in positive maternal and infant health outcomes. The results of an evidence-based review showed that a vegetarian diet is associated with a lower risk of death from ischemic heart disease. Vegetarians also appear to have lower low-density lipoprotein cholesterol levels, lower blood pressure, and lower rates of hypertension and type 2 diabetes than nonvegetarians. Furthermore, vegetarians tend to have a lower body mass index and lower overall cancer rates. Features of a vegetarian diet that may reduce risk of chronic disease include lower intakes of saturated fat and cholesterol and higher intakes of fruits, vegetables, whole grains, nuts, soy products, fiber, and phytochemicals. The variability of dietary practices among vegetarians makes individual assessment of dietary adequacy essential. In addition to assessing dietary adequacy, food and nutrition professionals can also play key roles in educating vegetarians about sources of specific nutrients, food purchase and preparation, and dietary modifications to meet their needs.

* Re. the definition of vegan, The Vegan Society, founded in 1944 by Donald Watson and others, inluded "the doctrine that man should live without exploiting animals" already in 1951.

(Donald Watson, who was a vegetarian for over 80 years, and vegan for over 60 years, died in 2005, aged 95.)