FTP, or File Transfer Protocol, allows people to upload or download files to a remote host (such as a server or another computer). There exist many different FTP clients, but FileZilla is probably one of the best. It is completely free to use, and there are hardly ever any issues.
Files are transferred over a TCP network protocol such as the internet. It has become a must-have tool for serious webmasters. In addition to being able to easily upload files to their websites, they can also use it for simple, secure, and regular backups of these sites.
It has been around since the 1980s and was first implemented by Abhay Bhurshan. It can be ran in both passive and active mode. If you really want to understand the nitty gritty details of how File Transfer Protocol works, we suggest that you take a look at it on Wikipedia here: http://en.wikipedia.org/wiki/File_Transfer_Protocol.
However, if you are a webmaster, you simply just have to install it and use it!