An authorization code is an extra form of security for a domain trade or transfer. This authorization code is unique for each domain, and is determined at the same time as when the domain is registered.
The transfer a domain to Nucleus, it is needed to supply this authorization code. This proves that you are allowed to transfer/trade this domain. The code itself can be requested at the current agent of the domain name.
Not every domain name requires the use of an authorization code. A .COM, .NET, .ORG and .ASIA require you to supply the authorization code.