Wit is what truly separates us from The Others. Now, for the definition. Being witty is not the same as being funny. Wit does more than imply your intelligence it screams about it. Wit means that you can think on your feet and that your brain keeps up with you mouth.
Some people are extremely witty while others have their moments.
Moments of great wit are cherished gems. A moment of great wit is worth a career of stand-up. Great wit gets quoted. However, the benefits of being book-smart are that even if you aren't all that witty and you don't think you're very intelligent you can at least be understood. This means an effort at proper grammar, fact-checking and relevancy.