Some websites only allow you to have one active login session at a time -- but Facebook isn't one of them. When you log into Facebook from a new computer or browser, all old sessions are still logged in. Facebook's settings allows you to review all locations where you've logged in. This allows you to make changes and remotely log out if necessary.
Checking Active Sessions
Open Facebook on a computer browser -- not on a mobile device -- and click the "Settings" icon in the upper right corner. Choose "Account Settings," then go to the "Security" section of the Account Settings page. You'll see an item called "Active Sessions," which should say something along the lines of "Logged in from Kansas City, KS, and 3 other locations," though the locations and number of sessions will vary. Click this to see all your current actively logged in locations for Facebook, Facebook Mobile and Facebook Messenger. Each session details the device used to access Facebook, the location and the time when the login session was last active.
Logging Out Remotely
Remove any sessions that use a browser, app or location that does not look familiar. Even if you end up logging yourself out, you can always log back in. Click "End Activity" next to an item to log out of Facebook on that device. The session will disappear from your active sessions after a few seconds.
Changing Your Password
You should periodically change your Facebook password to ensure that your account remains secure. If you're seeing multiple sessions you don't recognize or are worried about your account security on shared computers, now is a good time to do that. In the "General" section of the settings you can see the last time you changed your password. Click this item to update your password.
Login Notifications and Login Approvals
If you're the sort of person who only uses one or two devices to access your Facebook account, you can set up an extra layer of security to prevent unauthorized users from accessing your account. One option is to set up "Login Notifications," which sends you a message every time someone accesses your Facebook account on a new device. Another is "Login Approvals," which requires you to have a cell phone. With Login Approvals enabled, whenever you try to log in from a new location Facebook sends a code to your phone. You must enter that code before you're able to access your Facebook account.