FTP, or File Transfer Protocol, is a means of being able to transfer files from one computer to another. Usually FTP is used for transferring files to and from web servers. It is one of my favorite methods of uploading websites, scripts, files, and etc.
FTP uses a client and server program. The server program listens and waits for incoming client connections, and once a connection is established the two computers can communicate with each other and transfer files back and forth. A client program is needed to interact with the server (from a website designer/developer/manager's perspective) and upload/download files.
My favorite FTP client is FileZilla (note: FileZilla also provides a server program, but we're not going to be using that in this tutorial). It's free and it can do everything you would want to do with an FTP client - I've also never experienced any bugs or any other problems (that were not my own fault).
First, go to the FileZilla website to download the client program:
http://filezilla-project.org/