Many reasons can explain why we sing in the shower. The most obvious reason — the acoustics in the bathroom. We just sound better to our selves in the bathroom. Because sound more easily bounces off tile and walls in the bathroom it provides more reverberation and realism to add to vocal styling letting us sound more like we are in a concert hall or studio. And because of the relatively smaller space, it gives a significant boost to our voice while adding more bass, which alls goes to making our voice sound more powerful.
Most of us also imagine ourselves as a top vocal artist and where better to do that than in the privacy of our own bathroom. For most of us, breaking out in song in public would be quite embarrassing. The bathroom is the one place we can have our most private thoughts. Just imagine as warm water is cascading over our body. That water is relaxing you, reliving you of stress and overall making you happier releasing your inhibitions. Singing also makes you breath deeper, increasing your oxygen intake, which in turn adds to your improved feelings of relaxation. For some, may create a more meditative state that further improves your ability to relax.
No matter what the reason you sing, if it feels good, keep it up!