Balanced does not remove noise. Noise is random and in fact as soundhound mentioned, noise will actually go up (3 db I think) in a balanced configuration. This is because you have 2 input stages producing uncorrelated noise from the stage. What balanced does do is remove common mode signals from the signal pair. A differential input has a figure of merit referred to as CMRR, or commom mode rejection ratio. If the differential signal coming in had a 60Hz signal injected onto both +/- inputs from wire coupling, then the signal would be reduced by the CMRR. CMRR's are usually frequency dependant with low frequencies getting rejected better. This is good for audio as mostly your trying to get rid of hum. Since hum is often injected by power cables running near audio cables, the balanced can save some cable placement issues. I suspect there are cases where ground loop problems will be minimized by balanced too.

Hope this helps
Mike