Two-factor or multi-factor authentication is a service that adds additional layers of security to the standard password method of online identification. Without two-factor authentication you would normally enter a username and password. With two-factor you would be prompted to enter one additional authentication method such as a Personal Identification Code, another password or even fingerprint. With multi-factor authentication, you would be prompted to enter more than two additional authentication methods after entering your username and password.
There are many different methods of two-factor authentication from Microsoft, Apple and Google.
Here’s a video Google made about two-step verification basics, which provides a good idea of what’s involved.