From my favourite website on the world wide web, dictionary.com:
1. a shout of encouragement, approval, congratulation, etc.: The cheers of the fans filled the stadium.
2. a set or traditional form of shout used by spectators to encourage or show enthusiasm for an athletic team, contestant, etc., as rah! rah! rah!
3. something that gives joy or gladness; encouragement; comfort: words of cheer.
4. a state of feeling or spirits: Their good cheer overcame his depression.
5. gladness, gaiety, or animation: full of cheer and good spirits.
However, in my experience, when people sign off with “Cheers,” what they really mean is, “Fuck you.”