Multi-factor Authentication is a method of securing access to an online account, computer system or app by requiring users to provide multiple inputs of information in order to authenticate that the login attempt is genuine.
Simply put, a factor is just a way to convince an online service or computer system that you are who you say you are, and thus proving that you are the correct user and not a hacker or someone else without the rights to access your account.
The most common authentication factor that is used today is the username and password pair, which only makes use of a password to gain access to your account, making it a single-factor authentication. Having just a password to secure your account is extremely outdated and unsafe. A lot more online services are adopting a Two-factor authentication (2fa) method which is a lot more secure and highly recommended.
Two-factor authentication (2fa) is a method of establishing access to an account where you'll need to provide both a password and prove your identity with some other way to gain access to your account, usually via a separate email address or with the use of a mobile device.
The most common form of 2fa is in the form of the usual email address and password pair, with an added layer of security through the use of an SMS code that gets sent to your mobile device and only once the code has been submitted and confirmed to be correct, can the system confirm that it is really you.
Passwords have become increasingly less secure over the years, mainly due to poor user practices or data breaches and so more and more companies are insisting that we move to a 2fa to secure our accounts.
Verizon's 2017 Data Breach Investigations Report discovered that 81% of the accounts that were hacked were hacked because passwords were either leaked by being hacked from a companies server or because passwords were so weak (e.g., "passw0rd") that they were extremely easy to guess. With Multi-factor Authentication even these accounts would have been less likely to have been breached by hackers.