These days 'livid' usually means angry. Very, very angry. Really hopping mad, in fact. Originally, as Webster1913 points out, livid referred to a specific colour, a grayish-blue.
Probably the changeover comes from the fact that your face may change colour when you are angry. If you ever see someone who looks grayish-blue, they are either livid with anger or asphyxiating.
See angry, enraged, conniption fit.