This is how Facebook defines “Login Approvals”
What are login approvals?
Login approvals use text message (SMS) confirmations to make it harder for unauthorized people to use your account.
How it works?
When you try to log in using unrecognized computer, you’ll have to enter a security code that we text to your mobile phone.
“Login Approvals” is a security feature of Facebook that requires two-factor authentication from the user before user can access his account. Instead of just using a password, the user must input a verification code which is sent to their mobile. The “Login Approval” is a useful feature implemented by Facebook, just like google’s “two step verification” feature. However, it can become a problem if your phone is lost or you have no access to your phone. For example, if you travel to an area with no mobile reception, you will not be able to receive the code that allows you to access to your Facebook account. In short, If you don’t have your phone, you will not be able to login to your Facebook account from a new computer. However, you can still login to your account from a computer that has already been authorised. Two-Factor Authentication seems to be the next big thing to protect accounts from unauthorized access.