FTP stands for File Transfer Protocol. It's the most common method for web developers to connect to their web servers and upload / download web pages on their sites.
In order to use FTP you'll need an FTP client; a program that can coordinate the data stream between your computer and the web server. Technically you could use FTP by entering commands into your computer's command-line interface, but that's pretty tedious if you're transferring large numbers of files back and forth, as is the case with web developers.
Fortunately, there are plenty of free, easy-to-use FTP clients available. Some of the most popular clients are:
Core FTP – My personal favorite, Core FTP allows you to set up multiple profiles (a must for developers working on several different websites!) and can use regular or secure FTP. It can also resume an interrupted download or upload, which is extremely helpful if your internet connection drops in the middle of transferring a large file. Core FTP's main downside is the fact that it times out the connection after a couple of minutes, so if you post a page, review it, make changes with your HTML editor and return to Core FTP to upload the edited page, you'll likely need to reconnect to the site.
Filezilla – Another popular and free FTP client, Filezilla has a particularly user-friendly interface and allows simultaneous file upload/downloads for those blessed with a fast internet connection. Those of us who are not so blessed in the connection speed department can appreciate its ability to set transfer speeds based on time of day.
AceFTP – Boasting a Windows-XP style drag-and-drop interface, AceFTP has a particularly quick learning curve for new users who are used to Internet Explorer. CNET editors describe this program as having "rock-solid stability and speedy performance." Be aware that AceFTP will need to install its toolbar into your browser for full functionality.
Before you hurry to download any of these programs, check your HTML editor! Many of the popular editors include a built-in FTP client, so you won't need any additional software. On the other hand you might find a great HTML editor with a terrible FTP interface, in which case it might be worth your while to get a separate FTP client and use the editor solely for editing.