Something that's unappealing isn't inviting or interesting to you, like an unappealing bowl of cold brussels sprouts. Yuck.
If you've got to decide between cleaning the bathroom and taking out the trash, you could call those two unappealing choices. And if your family plans to vacation at a working farm instead of Disney World, that may also sound unappealing. Anything unappealing doesn't please you or catch your interest. This word is formed by adding the prefix un- ("not") to appealing, which can be traced back to a Latin root meaning "to summon."