Only when I have had to send something official to a government department and that has been the only option. I've had to search around for a friend who still has a fax machine. Other than that, I don't think they're in much use these days.
I think the last time I tried to fax something from work was a couple of months ago and it was so darn complicated with this new multi-fan-dangle machine that I couldn't work it out. I'm not bad with these things but this was just too hard for me. So I gave up, scanned it and emailed it. Sooo much easier to do.
A fax machine is a machine that electronically sends a page (or pages) of information to another fax machine either via a telephone number or designated fax number. If sending using the telephone number the person on the other end receives a tone indicating a fax is wanting to be received and switches the phone to "fax" mode and the information comes through the fax machine, or automatically if it's a designated fax line. It's not as popular now as emails have taken over and supposedly emails were deemed to be the saviour of our forests.