It's easy to check your Xbox reputation: just head to your account settings on the Xbox website. From there, you can view your current reputation level, as well as a summary of feedback you've received from other players.
Your reputation is determined by a number of factors, including how often you're reported for bad behaviour and whether or not you respond to feedback from others. If you want to improve your reputation, be sure to avoid getting reported and take time to reply to any negative feedback you receive.