Many children bite due to overwhelming emotions they are experiencing - whether its love, dislike, fear etc. Some children are more tactile and like to experience things through their mouth (its a sensory thing after all!).
Some chilren do it out of frustration, tiredness, hunger.
None of this is consolation for the bitten though.
You need to find out the triggers for the biting. You need to come up with a plan of action with parents in agreement about how to deal with. If you can figure out the triggers then you can intervene with distraction and divert the biter.
Other things to try while you are figuring the triggers are - swift removal of the biter (to somewhere safe and in sight/sound) - TONS of lavished attention on the bitten - making a point of saying I know that hurts, its mad you sad/upset etc.
Brief explanation to the biter - biting hurts/makes people sad etc.
A firm, calm, consistent approach
Its a 'phase' that many children go through as I am sure you know.