*ret(h)-

The core idea of this root was:

rolling, moving

It’s the origin of the Latin rota (wheel) and its small version rotula, which are the origin of words like rotate and (via French) the words role, to roll and roulette.
Also words like round and the German rund ultimately come from the Latin branch.

Role in the sense of character, role in a scene  comes from the fact that the texts of an actor were a roll of paper back Rome and Ancient Greece.