to be able to restore across the network Sql must run under an account that has network privileges. Local system has no such rights, being 'local' to the server. That is why you need to create a domain user account to run the SQL services under plus give that account rights to the server share (see manu's post).

By UNC manu means the full path to the network share, so if it is a share called 'share' on servera in directory c:\mssql\backups\dbname.bak use either

restore database dbname from disk = '\\servera\share$\dbname.bak'

OR

restore database dbname from disk = '\\servera\c$\mssql\backups\dbname.bak'