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Definition:

To "cast out" or "drive out" someone or something means to force that person or thing to go away.

The term "cast" means the same thing as "throw." To cast a net means to throw the net into the water.
In a figurative sense, "cast out" or "cast away" someone can mean to reject that person and send him away.

Depending on the context, other ways to translate this could include, "force out" or "send away" or "get rid of."
To "cast out demons" could be translated as "cause the demons to leave" or "drive the evil spirits out" or "expel the demons" or "command the demon to come out."