One who abstains
from all animal products
in their lifestyle
-- not just food. Such items include: meat
of all forms, dairy
, products which were tested on animals, etc.
Donald Watson was the first person to use the term "vegan" -- he coined the term. It was derived from the word "vegetarian" (as apessos points out below) when people (lead by Donald Watson) from the Vegetarian Society branched off to form the Vegan Society.
The goal of a vegan is usually to minimize the harm they do to animals and the environment. While total elimination of harm is nearly impossible considering our dependence on animals and animal products in our current society, much can be accomplished. Some people become vegan not for ethical or environmental reasons but for religious reasons.