GregM answered this fairly well above, but I'll try to add some more background and detail.
In most home audio systems, the analog signal between devices (e.g. from your dac to your preamp, or preamp to amp) uses an RCA cable. This type of cable has a single signal conductor and a ground conductor. The ground conductor is doing double duty here, providing both a ground reference between devices, and providing a return path for the audio signal.
In a balanced system, a balanced cable using XLR connectors is used to connect devices. These cables have two conductors for carrying the audio signal, and a separate ground conductor (often the shield). In this case, the audio return current does not have to share the same conductor as the ground connection, and any ground currents that may exist will not interfere with the audio signals. Ground currents might occur if, for example, the two devices that you are connecting are plugged into different outlets, or if one or more of the devices being connected has a poorly implemented grounding system.
The other potentially big advantage of balanced connections is their improved immunity to noise pickup, but this is dependent on properly implemented differential inputs.
It's possible to use balanced connections without using a balanced preamp, but the signals have to be converted back and forth between balanced and single-ended (meaning a single audio circuit path). I suspect that most home audio devices that have XLR connectors to support balanced connections work this way.
This can still have advantages in that ground problems are reduced and most of the noise picked up by the interconnect cable can be cancelled (assuming a properly implemented differential receiver on the device inputs). But it also adds extra circuitry that would not be required with normal RCA connections. So unless you have a noisy electrical environment (live near a radio transmitter, cell tower, etc.), RCA connections may be preferable.
A "real" balanced preamp has separate circuits to handle the two audio phases, so they don't convert the signals from balanced to single-ended and back again. This generally eliminates the unnecessary circuitry to convert back and forth, and also has the advantage of improving the signal to noise ratio and potentially cancelling some non-linear distortion products. The downside is that virtually all the audio circuitry in the preamp is doubled which will significantly increase the cost.
Personally, I'm a fan of fully balanced systems because of their improved noise performance, but they aren't for everyone.