Automatic ring back is a service offered by phone companies.
On making a telephone call to a number that is engaged, automatic ring back is a service provided by the telephone company whereby, when the called number becomes available, the caller is rung back, usually with a distinctive "ring back" ring.
When the phone is picked up, it calls the previously engaged number.
The service is typically invoked by keying a number on hearing the engaged tone.
[1] In the United States the service is often called Auto Redial.