If it is a windows client OS (like XP/Vista/7/8/8.1/10) computer that you are connecting to, you will take control of their computer and their session will go in to the background and they will see a locked screen, and that you are logged in. They can simply log back in to their own session, which will disconnect you. It's like the switch users process, none of their programs close, they just can't interact with them until they log back in.
This is one way MS makes money from businesses, selling windows server that can run remote desktop services (RDS) along with Windows and RDS client access licenses (CALs).
Edit: Scott has pointed out that since they are using the same user account, the other session won't go in to the background, it will simply be taken over, and the other person will either see a lock screen or be disconnected from their RDP session. Thanks Scott.