There are two similar setups - Network Home Directory users, and Portable Home Directory Users, both are linked to Open Directory user accounts.
With a Network Home Directory user a user logs in and accesses their home directory stored on a server, this does not result in a home directory being created on the client Mac.
With a Portable Home Directory user, a user logs in and this triggers creating a local user account linked to their network user account and also triggers the creation of a local home directory stored in /Users on the local drive, optionally it will sync the content of their matching network home directory folder to the local home directory.
It is possible to configure via Workgroup Manager MCX preferences, or preferably these days via Profile Manager which approach is used. It is also possible to present a dialog box when the user logs in offering a choice. If the portable home directory choice is made then thereafter each time the login that portable home directory will continue to be used. Portable home directories are particularly suited to laptops as they can be used even when the laptop is not connected to the network. Password changes between a portable home directory user and Open Directory can be automatically synced so that when you change the password on your client Mac it updates the matching account in Open Directory, remember with a portable home directory account a local account has been created. (Linked to the Open Directory account.)