An MMI Code is a sequence of digits that is entered into your phone to make it perform some special action.
These codes start and end with a * or # so they don't get confused with phone numbers you might want to dial. They're usually only valid when you're not on a call, so if you key one in while connected to your cellphone company's IVR system they won't be recognized. Some MMI Codes are dealt with by your phone - for example, there's usually one you can key in to find out what software version your phone has installed.
Most MMI Codes are sent to your Cellphone company as they are used to turn features on and off (Like call forwarding, call waiting, etc).