A fax is a machine that sends a scanned paper copy using a telephone line, and it's also what you call the document itself. When you send someone a fax, their fax machine prints it out for them.
You might need to send a fax when you're signing an important document long distance: for example, a lease or loan agreement might need to be signed, scanned, and sent as a fax. The word is a verb, too: "I'll fax that to you right away." It's short for facsimile, "exact copy," from the Latin root fac simile, "make similar." The growth of the Internet means that faxes aren't used as often as they once were.