A domain auth code is a 6 to 16 character code that's assigned to your domain name which is used to authorize domain transfers. This code is assigned by your registrar and works like password for your domain name
When you initiate a transfer registrar request, the registry will send you a transfer authorization request. You need to respond to the authorization request with your domain auth code in order for the transfer to work. Only transfer authorizations received with the correct domain auth code will be approved.
If your domain is registered with Doteasy, you can obtain your domain auth code via your Member Zone.