It used to be that only peasants laughed out loud, while the aristocracy and the Samurai laughed in a much more discreet way. There is a common view, dating back centuries, that showing other people your 'secret places', the inner spaces of your body such as the cavity of your mouth, was not done. Also, teeth are usually white, like bone. Bones are associated with death and thus, in ancient times, teeth were associated with death and not to be seen in daily life.
Conversely, the sight of bare teeth also seems to have been considered potentially too seductive. Married women were even known to blacken their teeth, in order to avoid attracting other men!
In Europe, laughing out loud is not considered inappropriate, but it is politer not too laugh too loudly in public places. Covering the mouth, however, is seen more as a sign of shyness or of trying to cover up your amusement, for example because what you are laughing about is a bit naughty.