This is a good question. If you are subscribed to a trader, then all his trades get copied. You trust him to make all the desicions on buying or selling. Although you can terminate copy-trading at any time.

Quatation from FAQ section: How do I stop subscribing to a trader?
Unlike traditional asset management services, we provide investors with complete control over their assets. Investors can unsubscribe from strategies at any time. Unsubscribing from a Trading Model can be done in the click of a button. Just click the Unsubscribe button in the investors strategy dashboard window, and all positions will be terminated and assets returned to your wallet.

Yes, please have a thorough read on the Covesting site, you may find more answers to the possible questions there.