The Skype application that comes with Windows 10 now has a notification area icon. It's great, but you can not right-click on the Skype taskbar icon and close it like a traditional desktop application. Skype does not give you an "Exit" option.
However, you can hide the icon of the Skype configuration window. Right-click the Skype icon in your notification area, then click "Settings" or open the Skype window, click the "…" menu button, and then click "Settings".
Click the "General" category and disable the "Show Skype in the Windows notification area (system tray)" option. The Skype notification area icon will disappear.
Note that users can still send you Skype messages if you are signed in, even if Skype does not appear in the notification area. To stop this, sign out of Skype. Click on the "…" menu in the Skype window and click "Logout" to do it.
If you do not want to use Skype, you can also uninstall it. Locate the Skype shortcut in the Start menu, right-click on it and select "Uninstall". Windows 10 allows you uninstall many other built-in applications that way too.
If you have multiple Skype applications installed and simply want to remove the built-in version of Windows 10, look for the Skype shortcut marked as "Microsoft Store Trusted Application" and delete it.
The traditional Skype desktop app has a "Quit Skype" option when you right-click on its notification area icon. This version of Skype works like the traditional Skype client you are used to.
That's pretty confusing, because the integrated Skype version in Store and the modern desktop version are almost identical, but the desktop version of Skype offers more features.