Many threads on this - check the archives. Unless you have long runs or a hiss/hum problem, RCA is fine.
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An unbalanced cable has two conductors (wires)--one for the signal, the other for ground.
A balanced cable uses two conductors plus the ground for a total of three. The extra conductor in the balanced cable carries an inverted version of the audio signal.
Its use is this: when the signal arrives at the amplifier, the inverted one is flipped over and recombined with the other signal. The cute trick is that any noise added by the cable is flipped too. Cable noise is positive in both wires; the final flip makes one noise signal negative and it cancels out the noise signal in the other wire.
Balanced configuration has real advantages for very long cable runs which can pick up a lot of noise, and it is pretty much indispensable for live recording. For shorter runs, it may or may not make a difference depending on your gear and your situation.
Also, balancing adds considerably to component cost, since the circuitry to produce the second, inverted signal at one end must be just as high-quality as the circuitry for the non-inverted signal, and so must the flipping and combining circuitry at the other end. Balanced wires are more costly than unbalanced, too, for equivalent quality.
So IMHO if you need it you need it, but better if you don't need it.
Lastly, it is unfortunate but some components which are advertised as balanced do not actually use truly balanced circuit configuration, although they do have the double signal (Cannon or XLR) connectors. Buyer beware!
Papi, as for your last question and using your example. If the integrated has balanced inputs only and the CDP only has single ended (RCA) you can use adapters to make the connections. This works, however there is a slight degredation in the sound. It is always better if you can avoid adapters. Also, not all components that have balanced connectors have the balanced circuitry inside. Just something else to watch for. Look for statements in the ads like "fully balanced" and such. If you don't find it in the literature, ask. As for BAT, I know their equipment is fully balanced and there are many other brands that are as well.
I know I will pay dearly for this but when I hook-up the Krell 280 CDP to my 400XI with Hero RCA ICs, tremendous amount of bass and warm sounding. As opposite, with Hero XLR I get more details and less "big bass", very balanced sounding. This is just my own experience with my own gears. I understand others will think otherwise.