It is the necessary evil of domain name ownership.  The official name is AuthInfo Code, but registrars use a variety of names:

• Auth Code
• Authorization Code
• EPP Authentication Code
• EPP Authorization Code
• EPP Code
• Transfer Key

What Is It?

No matter what name is used, its goal is the same – to protect you from an unauthorized transfer of your domain name.   The auth code is unique to each domain and is assigned by the domain registrar.  Before the AuthInfo code was put in place domain transfers were much easier, which lead to domain hijacking or people accidentally transferring to other registrars which would trick you into transferring.

Even today that practice is still employed by less then reputable registrars (who hasn’t received a fake “renewal” invoice by mail or email?) but with the AuthInfo code you can no longer simply transfer a domain by clicking a link.

Where Is It?

Tracking down the code can be a hassle – it’s not always the easiest thing to find on a registrars website, so here is a list of the the most popular registrars and their instructions for how to obtain the code:

Enom
Use the form below to look up your reseller and then contact the reseller to ask them to send you the auth code:
http://www.enom.com/help/reseller_lookup.asp

GoDaddy
https://support.godaddy.com/help/article/1685/getting-an-authorization-code-to-transfer-your-domain-name

Melbourne IT
http://support.melbourneit.com.au/articles/help/How-do-I-transfer-my-domain-away

NameCheap
https://www.namecheap.com/support/knowledgebase/article.aspx/258/84/what-should-i-do-to-transfer-a-domain-from-namecheap

Network Solutions
http://www.networksolutions.com/support/preparing-a-domain-name-for-a-transfer-out-of-network-solutions/

Register.com
https://forum.web.com/register/faq/#AccountInformation/What_Is_an_Authorization_Code.htm

Tucows
Use the form below to look up your reseller then either contact them to ask them to send you the auth code, or ask them send you your Tucows control panel details so you can login and obtain it.
http://www.tucowsdomains.com/management-and-passwords/findprovider/

Yahoo
https://help.yahoo.com/kb/yahoo-domains/retrieve-authorization-code-sln17886.html

Once you obtain the auth code it will be used during the transfer process to approve the transfer of your domain name to the new provider.  Normally this involves clicking a link sent to your email and you will be presented with a confirmation form where you will enter the auth code.

If you need the instructions for a registrar not listed here, a Google search for “[provider name] get auth code” will usually bring up the instructions in the first couple search results and you will be on your way to approving your transfer.