Pianos are tuned to an equal-tempered scale-- essentially (and, of course, over-simply) you "spread out" the "out-of-tuneness" that results from the fact that the Western 12-tone chromatic scale doesn't fit inside a perfect system of frequency ratios. See here for lots of math that I don't understand at all:

http://en.wikipedia.org/wiki/Equal_temperament

As a side (historical) note, one of the earliest champions of Equal Temperament (or Well-Temperament) was Bach, who wrote The Well Tempered Clavier as a kind of advertisement for this tuning system. Prior to systematized equal temperament, it was impossible for an instrument to play in all 24 keys without being re-tuned. On a Well-Tempered instrument, you can play straight through all 24-keys without stopping to be retuned.

Singers (and brass players, and any other instrument that allows for fine, sinlge-cent level tuning) often use a different system called Just Intonation:

http://en.wikipedia.org/wiki/Just_intonation

Just Intonation is "more in tune" than Equal-temperament, but it is not noticeable by most people. I teach music for a living and have a degree in music theory and I have a very difficult time telling the difference.

EDIT: Yes, I did oversimplify by conflating equal temperament and well-temperament, but in the modern debate, they do tend to get lumped together.