The thing to understand here is that "balanced" is an overloaded term, such that it has two different (but similar) meanings that are often confused or mixed.
Balanced in pro audio and signal transmission means that there are 3 lines: positive, inverted, and ground. This allows the positive signal to be added to the inverse of the inverted signal to cancel out line noise. It also implies, but does not require, a +4 standard for signal level, which gives an extra 12 or so decibels of audio over the consumer unbalanced standard, which should result in a better signal to background noise ratio for the same content.
Balanced in headphone wiring means removing the common ground between the two channels, and replacing it with separate grounds that carry the inverted signal. This is believed to decrease channel crosstalk, and therefore increase stereo separation. Whether that belief is factual is dependent on the two signals being compared. One thing that is generally true is that balanced amplifiers use high end designs, and generally sound really good, though it is arguable whether any of this goodness is actually due to having balanced outputs.
(My apologies to people in this thread who already know this stuff. I thought having a clarification may be useful for some.)
Balanced is the same signal in pro audio as it is when driving a headphone: there is a non-inverted and inverted signal, both referenced to ground.
However, in proaudio when you are sending a balanced signal to a balanced input, At the receiving end, the inverted signal is subtracted from the non-inverted signal.
This creates a signal which is 6 dB higher than the non-inverted signal alone, in addition since you are subtracting the inverted from the non-inverted, then you are also rejecting the noise picked up by the two signal leads.
In headphones, the headphones themselves are not rejecting noise, they are just receiving a 6 dB hotter signal. You could argue thus actually does nothing to improve the signal but create twice as much distortion and double the output impedance of the head amp.