Private lines is a Enterprise Voice feature added to Lync Server 2010. Private lines are a secondary, incoming only number assigned to an existing Lync user. A private line is usually used by company executives. Calls to the private line always ring through even when the user sets their status to Do Not Disturb, with a special ringtone. Also private line numbers do not appear in the address book and are not searchable.
Private lines are configured through Powershell
Set-CsUser -Identity "sip:email@example.com" -PrivateLine "Tel:+14255551212".