A FTP client is a program that connects to a FTP server and allows the user to transfer files to and from the server. There are many reliable, free FTP clients out there, so there is no need to pay for one unless it has an advanced feature that you desperately need. FTP is often faster and much safer than transferring files over a HTTP file manager, especially when transferring a large number of files. In order to use a FTP client, you need to know your hostname (domain name), FTP username, and FTP password. If your hosting account uses a control panel such as cPanel or Plesk, then the FTP username and password is often the same password you use to login to the cPanel or Plesk control panel.
If you transfer files on a regular basis from your personel computer, it is often a good idea to create a "profile" to easily connect to your FTP server. A profile will save your login information so that you do not have to type in your information everytime. However, make sure you only do this on a personal computer (one that nobody else has access to), as anyone else using that computer would have access to your FTP server, and therefore all your files.