A dedicated server;
In terms of software, all it does is the serving - i.e. theres no graphics, just a basic window and thats about it. This is free. You can run this on almost any machine (both windows and linux (via wine) - I've not yet tried macs [as I dont have one]). The advantage is that you don't need a very powerful machine (as low as 200-300MHz can run a dedi server).
In terms of hardware, a dedicated server is usually a pc, or rackmountable server, that just sits online and serves things; websites, LFS games, you name it. Note: this is not required to run a "dedicated LFS server", you could run it on your normal PC.