FTP stands for File Transfer Protocol.
It is a protocol that allows you to transfer files from/to your home computer to another.
For example you will use FTP to upload phpBB files and MOD'ed files such as eXtreme Styles Mod 'includes/template.php'.
To FTP, you will need an FTP client - search results on google can be found here You will also need a FTP username, FTP password and an FTP addess to connect to, such as ftp.your-domain.com
Important: Users using free phpBB hosting, WILL NOT have FTP access so you not be able to change any existing files or install: mods, styles, images such as ranks, smilies etc.