Butter is considered to be a dairy product and an animal byproduct which is what is not allowed on a vegan diet. Those who consider themselves to be true vegans do not eat anything that is derived from an animal, including butter. Since butter is essentially derived from the udders of a cow, it is considered to be an animal byproduct.
There is however alternatives such as almond or soy butter which are both very popular with vegans. Those who are starting to get into veganism will definitely want to take a look at some of the recipes that exist for converting certain foods like butter into a more vegan-friendly form.