Short answer, no, butter is not vegan. But if you're asking this question, then you probably are in need of some more information to help you understand why butter is not vegan, and, depending on why you're asking, you may need to know more about what exactly, a vegan is, or what, exactly, butter is (or what it means when you hear or see the words "vegan butter").
What Is a Vegan?
A vegan is a person who does not eat any food which came from an animal.
This includes meat, of course, but it also includes eggs, dairy products, and some other animal byproducts as well. So, to clarify, vegans do not eat any kind of meat (beef, chicken, fish, shrimp, hamburgers, etc.), any kind of dairy products (milk, cheese, butter, ice cream, etc.), or any foods containing these products, such as pepperoni pizza, plain cheese pizza, omelets, egg salad, etc. Keep in mind that this is different than a vegetarian, which is someone who avoids all animal meats, but will usually consume eggs and dairy products.
The word vegan is also used as an adjective to describe foods which are free from animal products and made entirely from plants, such as fruits, vegetables, beans, lentils, whole grains, and nuts and anything made from these foods, such as hummus, tofu, and meat substitutes.
What Is Butter?
Butter is made from cream, which is the higher-fat part of milk, which comes from a cow.
Traditionally, the definition of butter is very simple, and theoretically, butter contains little else other than the cream, but if you go to a grocery store, you will see dozens of different products labeled "butter". Because food manufacturers add so many different food additives, chemicals, and fillers, it can be a little confusing as to what, exactly, is what.
So, to summarize, since butter comes from cream, which comes from a cow, and vegans do not eat any products which come from animals, it's clear that butter is not vegan and should be avoided by anyone eating a vegan diet.
So What Is "Vegan Butter"?
When you hear or see the word "vegan butter", it's a bit of a misnomer and a shorthand for what's really being discussed. A better and more accurate name would be "vegan substitute for butter" or a "vegan butter-like product". To avoid this confusion, many people label it as "vegan margarine", as it's more accurate.
Vegan butter is not actually butter. It is not made from milk, or cream, or any product coming from an animal. Usually, vegan butter is made using oil and other ingredients to create a product which looks, acts, and tastes like butter, but is not actually butter.