Seriously though, it's nice to see someone rather clueless (sorry Erik) about technology when I realize how clueless I am about certain things..
To answer your question, the abbreviation was correctly explained by Fanatic. FTP is a means of transferring files between computers, it requires a server and a client. In the typical sense, a server will allow numerous clients to browse and download files at the same time, it is up to the server administrator to set whichever restrictions are of interest. Which in turn implies the server should have adequate bandwidth to support the traffic it entertains at all times.
In order to access an FTP server, you need an FTP client, such as Cute FTP, usually the default settings will do, you may need a username and password though.
To make it simple, Nekton had an FTP server open most of last year, a number of people downloaded files from his computer using an FTP client of some sort.
CuteFTP is cool tool. You can download that program from www.downloads.com . But it's only a trial version.
The one I use is WS-FTP. Also another cool FTP tool.
Why I use them? So I can upload my files from my computer to my server. I know that if you have a web account, like Fortunecity, you will need an FTP prgram to upload (or download) your files, cos they don't provide the facility to upload from their site.