Hi Alex,
A "headless" user is one that is not associated with an actual person. This useful as it allows you to create users that are persistent in a database and these headless users are the ones who own feature classes, feature datasets and tables. For example if you are the owner of a feature class in a eGDB and you happen to leave the organization you're working for they will want to delete your user account for security purposes. However if they delete your user account in the database all the feature class your account owns would also be deleted. However if the feature class is owned by a "headless" user and not by your user then when you leave the organization they can delete your user account without risking the feature class being delete also.
Cheers!
