To protect a user from unauthorized Facebook login attempts, Facebook can alert the user of suspicious activiity. This is done with a feature called Login Notifications. If you want to be notified of the login attempt before Facebook grants access to that login, you want to enable Login Approvals. In addition, you can also view recent login sessions in Active Sessions. All these features can be found in the Security area of your Account Settings.
With this feature, you can opt to receive alerts whenever there is a login to your account from a new device; that is, a device such as a computer or mobile phone that you have yet to identify as your own on Facebook (via a previous login attempt while Login Notifications is enabled). You may need to identify several devices or browsers that you use before Facebook is trained to recognize them all. After that, Login Notifications becomes useful for detecting unauthorized access. You can choose to receive notifications via email or text or both.
This feature takes notifications a step further: Not only do you get an alert when there’s a login attempt, but Facebook won’t approve it either unless you tell it to do so. You will need a mobile phone number for this, one that is linked to your account. Whenever you attempt to log in from a new device, Facebook will send a verification code to your phone and you enter it at the Facebook login home page. You must also identify your own computer to Facebook so it will know when you are logging in from your own device or an unfamiliar one. This requires cookies. Make sure your Web browser is set to store cookies, unless you want to enter a verification code every time you log into Facebook via your own device(s).
Finally, Active Sessions is a log of your recent, open sessions on Facebook. Use this if you suspect someone else may have used your account, or when you forget to log out of Facebook from another computer or device. With Active Sessions, remote logout is possible.
To access these features, go to Account Settings (click the arrow at the top-right of the Facebook page first) and then go to Security.
See also Facebook login help.