Multi-factor authentication (MFA) is a method of adding additional security to your account. The first "factor" is your usual password that is standard for any account. The second "factor" is a verification code retrieved from an app on a mobile device or computer. Read more about MFA.
If you encounter a problem with your MFA device and lose access to your recovery codes, you will be locked out of your account and will have to prove your identity to cawikimedia.org. If they deny your request, it is impossible to disable MFA and you'll have to create a new account. Detailed help can be found here.