Having a group with your own username gives you an extra bit of privacy, it restricts who can access your files a bit more.
In the file permissions you have three sets of permissions: Owner, Group and Others.
All files/directories have an owner and a default group owner.
If your home directory is owned by you and the group ownership is set to "users", which is typically a group that all users are added to, then that would mean that the "owner" permissions on files and directories in your home directory are applied to you.
The group permissions on files/directories would apply to any all users in the "users" group and the ‘other’ permissions apply to any other users who are not you and are not in the "users" group.
So your files are accessible to you, and other users on the system who are in the users group get group access to your files, and anybody else uses the more restrictive "others" permissions.
Now, consider this. If your home directory is owned by you and the group owner is a group with your username - which is a group which only has you as a member, that means the owner and group permissions on all of the files/directories apply to you and you alone. All other users on the system can only use the "other" permissions.
So having a group with your name, which only has you as a member is a way of further restricting who can access your files!