Definition: Domains are hostnames that identify Internet Protocol (IP) resources such as web sites. They provide a human-friendly, easily recognizable and memorizable names to numerically addressed Internet resources.
In SmugMug terms, it allows you to use a unique custom domain like www.example.com instead of your nickname.smugmug.com URL.
Instructions for the basic SmugMug domain setup can be found here: http://help.smugmug.com/customer/portal/articles/93340
The basic setup for a domain like www.example.com is currently:
www CNAME domains.smugmug.com and @ A 22.214.171.124
For a subdomain like photos.example.com you just need the CNAME record
photos CNAME domains.smugmug.com
In either case, when using a domain to point at a SmugMug account, the CNAME must point at domains.smugmug.com