A YubiKey is a hardware based MFA device that you can use for a multitude of applications. Similar to when you get a text message for a verification code or use an authentication code from an app on your phone, the YubiKey works by plugging the device into your computer/phone or, on some models, tapping it on the back of your phone via NFC. After you enter your username and password, you will get a prompt to plug in your YubiKey and verify that it is actually you and then you will be logged in.
It supports many applications and vendors along with a large amount of protocols. The main reason for using it compared to other MFA modes is that it is extremely hard to impersonate, spoof, and brute force.