Their fax number gets used as the e-mail/fax address. They get a fax from you and you get an e-mail from them after they have faxed to whatever number you are issued by the fax service. When I was an e-mail adminsitrator I built one of these systems for my company to augment e-mail and reduce the cost of owning fax machines.
We had a T1 trunk for inbound into a brooktrout board that muxed T1 signal. The inbound fax was turned into a tif file attachment to a simple mail file and routed via gateway to the e-mail server and your mailbox. The reverse was you used a phone number as the address and the e-mail system routed that to the fax server to process as an outbound fax.
You no longer have to own a box in your house. Just have access to the internet. The only problem is now you have a layer of human ineptatude(tech support) between you and any problem that has to be solved. One of the biggest ones is if your customer has an older fax machine that does not like the hand shake protocol from the fax services digital system. The service is cheaper technicaly but, keep an old fax machine handy incase one of your customers home machine doesn't like the fax services digital wonder board.
People with lots of money very often use fax because it is secure and accepted by banks, the legal system and the IRS as a secure communications standard. Whats the new world record for hacking your cell phone at a Starbucks now...5...15...25 seconds?