AFS is short for the Ardrew File System. Basically AFS is distributed network file system. Remember, a file system is simply a collection of files and directories assembled in such an order that the make sense to the operating system. So AFS is a way of keeping track of your files over the network.
Well you as a user are able to get to your files using any computer that has an AFS client installed on it. All of the lab computers: Windows, Linux, IRIX, and Mac all are capable of reading this file system. So as far as you the user is concerned files that you write to space within your account will be accessible to you over the network from any of these computers. No need to store your information on a floppy and carry it between machines.