Wake-on-ring
Wake-on-Ring or Wake-on-Modem is a specification that allows supported computers and devices to wake up or turn on from a sleeping, hibernating or soft off state, and begin operation.
The basic premise is that a special signal is sent over phone lines to the computer through its dial-up modem, telling it to fully power-on and begin operation. Common uses were archive databases and BBSes, although hobbyist use was significant.
Fax machines use a similar system, in which they are mostly idle until receiving an incoming fax signal, which spurs operation.
This style of remote operation has mostly been supplanted by Wake-on-LAN, which is newer but works in much the same way.
Additional resources
Category:BIOS
Category:Unified Extensible Firmware Interface
Category:Remote control