Like Charlie said, 'balanced is king'. I like to explain the operation algebraically, but first, it's important to remember that a balanced system's benefits don't really come to fruition unless a balanced send and a differential input are used; luckily, this is the common practice.

What do I mean by this?

Well, the term 'balanced' also refers to the fact that the signals on pins 2 and 3 (of an XLR) are effectively the same, but of opposite polarity. The easiest way to picture this is to think of a single-frequency sine wave on pin 2; the signal on pin 3 is the same frequency (in this example) and the same magnitude, but it is 180 degrees out of phase with respect to pin 2. In other words, for every 'peak' of the sine wave on pin 2, there will be a 'trough' on pin 3 of the same magnitude (but again, of opposite sign). Thus, the signals are balanced with respect to ground. Output (driving) impedance does indeed play a role, but the biggest factor (assuming that the impedances are equal) is the fact that an inverted version of the signal on pin 2 is on pin 3.

Enter the differential input amplifier...

Most TRS/XLR inputs are equipped with a differential stage - the first thing that the balanced signal sees. By definition, a differential amplifier subtracts one signal from the other. Here's where the algerba helps to understand the matter.

Suppose that induced noise in the balanced line (such as from AC mains near by) is called "A". Now, suppose that the signal on pin 2 is called "B". Since we know that pin 3 is the same magnitude, but opposite phase as the signal on pin 2, we can call this signal " - B " (that is, 'negative B' or 'minus B').

So, given that the difference amplifier SUBTRACTS pin 3 from that of pin 2, we get this:

Output = Pin 2 - Pin 3

But what is on pin 2 again? Well, we said that we could call the noise "A", and the signal "B", so algebraically this yields Pin 2 = (A + B). However, Pin 3 = (A - B).

Thus we get the following:

Output = (A + B) - (A - B)

Which yields

output = 0A + 2B

That is, if our signal on pins 2 and 3 were both 1 volt, we would see 2 volts of signal at the output of the difference amplifier (effectively a 6 dB gain). However, because the induced noise is the same (in magnitude and frequency) in pins 2 and 3, the difference amplifier effectively 'rejects' this noise - you will see this cited in many specs as CMRR (common-mode rejection ratio, and it is usually expressed in dB because the amount of rejection (for noise) is huge, thus the logarithmic scale).

So why...physically...does the induced noise go away? It 'goes away' because the noise that is induced in pins 2 and 3 is the same magnitude AND phase, whereas the SIGNALS on pins 2 and 3 are equal but of OPPOSITE phase. Remember that due to the propogation velocity ('c') of EM waves (3 e8 m/s...that is, the speed of light) any induced voltage into the balanced line will effectively be THE SAME on pins 2 and 3. This is because wavelength = c/f, so effectively this means that a 60 cycle waveform will be = 3E8/60 = 5E6 meters in length. Now, because the wires are (relatively to a wavlength of a 60 Hz field) effectively in the same spot (physically), there is no gradient seen by the conductors (the wires carrying the signals on pins 2 and 3) in the field. As a consequence, the induced noise in both pins 2 and 3 will in fact be the same in terms of magnitude and of equal importance, phase. Incidentally, this is also why in communications lines it is common practice to twist the pair of wires together (i.e. shielded twisted pair), because this helps minimize the physical space occupied by the conductors, and thus, makes them 'see' the smallest gradient possible...and thus...the smallest amount of voltage is induced in the wires.

The other side of the balanced kingdom comes from having a line driver that has a relatively low output impedance as well (remember - a low impedance source can drive a high impedance load, but a high impedance source cannot drive a low impedance load). Because the driving point is relatively low in impedance, this makes the cable capacitance 'seen' by the driving and receiving points less of an issue than it is in unbalnced (i.e. single-ended) lines. This is why, apart from noise pick-up, long runs through a typical RCA type connector will result in top-end roll-off (i.e. a loss of treble), because the capacitance of the cable (which is a function of its capacitance per unit length) really adds up in a long cable. This is why at large concert venues there is always a 'snake' consisting of many shielded-twisted pairs running from the mixing console to the stage (signals in), and from the mixing console to the dividing networks and amplifiers (signals out) and ultimately, out to the speakers. Were it not for balanced lines, this would not be pssible (if we wanted a noise-free signal).

So if you have a balanced driver, but you have an unbalanced load, then as Chralie said, you can take the signal from pin 2 (using pin 1 as reference) or from pin 3 (which will be out of phase with respect to pin 2) and use ONE of those, using pin 1 as the 'ground'. However, because the input to which you rea making the connection is NOT differential, then the noise rejection benefits of a differential input stage will be lost.

One other approach to driving an unbalanced input with a balanced signal (and this works quite well) is to use a high quality audio impedance matching transformer. These typically have a 3-pin XLR female on one end, and a 1/4" T/S (tip-sleeve, i.e. a 'mono' 1/4" plug) on the other end. From there, you could use a 1/4" female to RCA male (as short as possible) and thus, you would have the benefits of a balanced line going to your (distant) amplifier. You can find such transformers for around $30 or so a piece, and barring that, you can use an active solution - lots of companies make these (Audio Control being one of them) and they usually work extremely well. That is, they accept a banalced line input, and provide an unbalanced RCA-type output. These 'active' devices rely upon op-amps to perform the difference amplification and subsequent impedance buffering (and conversion to single-ended outputs), but some of them have less than optimal filtering capacitance in their power supplies, and thus (paradoxically) with poor filtering you are likely to get some 60 and 120 Hz hum (though usually at least 40 dB down with respect to the signal)...so my advice would be to look for the 'good ones' via respected customer review sites, preferably by people who know a thing or two about audio.

NOTE: If you are going to go this route, be careful to specify a matching transformer - there are adapters out there that do not have the transformer element, and these can look a lot like a transformer (often having the same or similar form factor) but do not provide the same function.

Conversely, the advanatge to using a matching transformer is that it is 100% passive, so it's not possible that hum will be added due to poor filtering. On the other hand...it is, after all, a transformer, and that means they are subject to non-linearity (I'm not talking about frequency response...I'm talking about linearity), hysterisis and the like, and some will claim they don't like the effect that they have on sound quality - like all subjective matters, you have to draw your own conclusions there.

Balanced lines are great - especially if you have dimmer packs (for lighting) in the home. Dimmers are notorious for generating lots of radio frequency interference (RFI) which often cause an audible buzz in the audio line, and many times, this is the simplest, cheapest, and most convenient fix (rather than moving your components away from the dimmer locations etc).

Mark