Log out and you'll have to enter your password the next time you want to access your account from this device. This is the recommended way to protect your account from other people who use this same device. This also takes some steps on the backend to protect your account from the generic Internet bad guy who's out there cruising the network, looking to steal anything he can.
When you log out from one device you won't be logged out from any other device.
If you don't use the "Remember Login" option when you log in then instead of using this Log Out page you can just close all BibleStudy.tools tabs and windows, and next time you log in you'll need to enter your password again. This protects your account from other people who use this device, but not from the generic Internet bad guy. If you do use the "Remember Login" option then closing all tabs and windows does nothing to protect your account, because anyone with access to your device can also access your account for the duration of a remembered login.
Note that the term "device" here might not mean what you expect. For example, you can log in using the Chrome browser, the Firefox browser, and the Edge browser on the same computer at the same time, and you're then logged in from three separate devices as far as BibleStudy.tools is concerned. If you Log out from one browser you won't log out from other browsers. Also, if you clear a browser's data then the next time you log in from that same browser BibleStudy.tools considers this a new device. Use the Login Devices page under the Account menu to see all the devices BibleStudy.tools has recorded for you.