Humidity does go up when it rains... as for why it sounds better:
As the humidity increases, speed of sound increases and sound power attenuation (by absorption) decreases. All because air density decreases as the relative humidity increases. This is a possible explanation; but I tend to favor the one that says sitting in your cozy listening room on a grey rainy day is one of the best places to pass the time watchin' the ions dislocate some surfaces - and the music just sounds better :)