Headless often means software that has no graphical interface, and can run in the background. These are usually server software, or something that can run as a server.

The headless build of Factorio is just the multiplayer server, so you can't play with it, but you can run it so that you and your friends can connect and play on the same same file.
The normal build can host the server too, afaik that too allows to be started with a CLI command, but the headless version is probably more efficient when you don't need the GUI.