Appeal means to ask, or address. If you appeal to someone's better nature, you're asking them for mercy. If a shirt doesn't appeal to you, you could also say it doesn't "speak" to you, or more simply, you don't like it.
Appeal also means to call upon a higher court to review a lower court's decision. If you appeal a court's conviction of you for shop lifting, you're asking a higher court to throw the decision out. Appeal descends from the Latin appellare "to address, call upon."