unbalanced connectors are the plain old rca connectors....there is a center conductor surrounded by a shield...the shield is the other conductor of the signal...
balanced connecotrs are xlr connectors or trs connectors...the + and - are a twisted pair of conductors and the ground is the shield surrounding the pair...
balanced connectors are used on high end preamps and amplifiers as well as most professional audio equipment...generally they tend to be quieter than unbalanced connections....
if you have a choice on your equipment i would recommmend using your balanced connections...
Balanced is also the way to go if you want to keep your speaker cable short by placing your amp near your speakers. Running long runs from your preamp to amp with balanced is better than running long unbalanced runs.
Balanced helps create a cleaner signal free of humming and other interference, and is typically used in pro-audio applications (e.g. the sound system at a concert.) Balance becomes important there because there is so much high power equipment around, and sometimes the cabling between the stage, the mixing board, and the amplifiers can be much longer than that found in a home audio environment.
If you are hooking two pieces of equipment together, and both have balanced inputs/outputs, then go for it and get the appropriate balanced cable for the link. For example, I have a balanced TRS interconnect between my BFD equalizer and my Samson 1000 subwoofer amp.
Very few home audio components have balanced I/O, so if yours doesn't, I wouldn't worry about it.