Not my words, but a google search found the following, which seems like a believable explanation;

"What's the difference between balanced and unbalanced connections?"

An unbalanced connection is what you have in normal consumer audio line-level connections. For any given signal, such as your left channel feed, you have a "hot" and a "ground" connection. The ground is normally in the form of a shield braid or foil wrapped around the "hot" connection. The ground connection remains at zero volts with respect to, well, ground - its level is the reference level for everything else. The "hot" wire is driven with an AC signal and at different times goes both positive and negative with respect to the ground wire.

Now the problem with unbalanced connections is that they're very subject to noise pickup, esp. in high-gain circuits like mic feeds. The "hot" wire acts as an antenna and picks up stray RF; it's also subject to both capacitive and inductive coupling to other nearby circuits. The inductive coupling can work over distances of several meters if there are heavy AC currents being used nearby (like the lighting in a TV studio). The shielding incidentally helps against capacitive and RF pickup but doesn't do a thing against inductive pickup.

In a balanced connection there are two signal lines and a ground shield. The two signal lines are designated + and -, or "hot" and "return", or "live" and "return", or some such terms. The desired signal is sent down both wires, but at opposite polarities. The + lead is the same signal as what would be on the "hot" lead in an unbalanced connection. The - lead carries the same signal, but at opposite polarity to the + signal. The ground shield may not even be connected at both ends of the cable - in fact it is often left unconnected at the receiving end.

Now here is the trick: the receiver for a balanced connection pays attention only to the DIFFERENCE between the two signal wires. This is called a "differential receiver" and for this reason you usually hear the terms "balanced" and "differential" used in close proximity. Well, noise picked up by the cable will tend to be picked up equally by the two signal wires. Since the receiver pays attention only to the difference, the noise is rejected. This is called "common mode noise rejection" because it is the rejection of noise that is common between the + and - signals.

If that seems impossible, consider a numeric example: Suppose the waveform at the moment is at +.5 volts in the positive wire and -.5 volts in the negative. The receiver does the "differencing" and emits 1.0 volts.

Now add 0.5 volts of noise to each wire, so the signal levels are 1.0 volts and 0 volts. The difference is still one volt!

There's more, but by the time I'd read the above, I understood.

Good question, glad you asked it. Now I know too.

Note the led matrix that shows exactly how the cable is wired and if any wires are reversed.  It can also sense phantom power and send a test tone.  For under $30.00 bucks it's a handy investment that you'll wonder how you lived without.