A Villain is a character in a story who the reader does not want to succeed in his/her/its goals. It may be the same as the antagonist, though not necessarily. The villain may in fact be a protagonist or main character, if the story is about the villain. Often, however, the protagonist and/or main character will be opposed to the villain.
An unnatural, unrealistic villain is referred to as a Dark Lord.
Conversely, a truly good villain should have a substantial and reasonable motivation for what they do and believe with all their heart that what they are doing is right. To use a historical example, Adolf Hitler may be known as one of the most cruel men the world has ever seen, but he believed that killing innocent Jews would make the world a better place.