It’s possible to run more than one Skype account on your computer at the same time. This might be useful if you have, for example, a Skype account you use for work and another account just for personal use. If you want to be signed in to both accounts at the same time, you need to start a new instance of Skype.
Be aware that if you have multiple instances of Skype running, you may need to use the Task Manager to close Skype.