Closing the Skype window just minimizes the application to the system tray.
As seen on the system tray(Bottom right on your monitor), you are still logged in to Skype and active(online).
To log yourself out, click ‘Skype’ on the menu and click ‘sign out’. and/or you can just close the application by right clicking on the Skype system tray icon(Shown in image above), click ‘Quit’.
Did you notice that whenever you open Skype, you automatically get logged in? This might be because you chose to ‘Sign you in when Skype starts’.
This is not good to have this in a public computer where others access the same system.
To change this
- Sign out of Skype
- Uncheck ‘Sign me in when Skype starts’ and log in again.
- 7 Skype Tips for Power Users (howtogeek.com)
- For Windows 8, Skype gets a full makeover (reviews.cnet.com)
- How to create a free Skype account (with pictures) (upcommunityblog.wordpress.com)