A fax number is a phone number that can be used to contact a fax machine. It looks exactly like a regular phone number.
Fax machines communicate over the phone network to send and receive information. They use audible tones to send and receive information.
Many offices have both a fax number and a phone number. Although fax operates over a phone line, it is a different phone number as fax services can interfere with services such as voicemail.