Tiles in your bathroom are hard objects which do not absorb any sound, but bounce it back, creating a powerful and loud sound. The hard and soft materials normally existing in a bathroom are reflectors, which is why your voice gets amplified like in a studio. It is this highly aural effect that makes one feel like singing in the shower.
When the showerhead is your mic and you are belting out your favorite tune, of course you sound better in the shower. Why? Because your voice bounces back and forth in the small space confined by better acoustics. The sound is enhanced, given a boost, and the not-so-good sounding notes in your voice are leveled out.