They realy ought to call it "balanced differential", not just balanced: it'd make it a whole lot easier to search for...
Basically, balanced = "push-pull". Unbalanced = "push only".
Balanced differential transmission drives one conductor with one polarity (the XLR's pin2 swings positive) and the other with the exact *inverse* of that signal (pin 3 swings negative). This allows the receiving equipment to look at the difference between the signals on the pair (differential mode), and reject any signal that is identical on both conductors (common mode). The whole idea of "balanced differential" signal transmission over a shielded pair of wires is that both conductors experience the *exact* same electrical and noise environment (which is also why they are so precisely twisted, in good cable). That's the magic.
Here's gross oversimplification. Just for grins, imagine a balanced line that has a signal that just happens to be exactly +500mv on pin 2 and -500mv on pin 3 at some point in time. Imagine that that line runs right under a computer monitor, whose mondo deflection magnets induce +3v of noise in both the pin 2 and pin 3 lines. The receiving equipment subtracts the voltage on pin 3 from the voltage on pin 2: ((500mv signal + 3v noise) - (-500mv signal + 3v noise)). This leaves 1v of signal (500mv - (-500mv)), and 0v of noise (3v - 3v): the noise cancels itself out because it is *common* to both signals, and the equipment only cares about differential.
If you were to shield the conductors separately, or run them as separate single-shielded unbalanced cables (like a pair of guitar cables run more or less side by side), the electrical environments of the two conductors would *not* be identical, and differentially-coupled noise allowed by the imbalance will become impossible to distinguish from the signal you're trying to send. In our example above, that might be 2.8v of noise on pin 2, and 3.1v of noise on pin 3. Whammo: you now have 0.3v of differential noise that gets added to your 1v differential signal, and there's no way to know which is which. No joy. Gotta make the environment as identical as possible for best noise rejection, which is why that pair is twisted and shares the single shield (pin 1 on your XLR, or sleeve on your TRS).
The rejection is never perfect for a whole boatload of reasons, which is why we still have to chase ground loops, noise and *cruft* out of our rigs. However, balanced differential signal transmission is a *vast* improvment over single-ended (unbalanced, like from your guitar to the amp)... And we didn't even need to talk about impedance (or any of that other jit that plastic-pocket-protector folks like me love so much) to get a basic handle on why.
Hope that helps.
