To make an FTP connection, the server needs to know on which port to talk to your PC.

In active FTP (which was designed before firewalls were common) your PC tells the server "this is the port you should talk to me on," and the server attempts to connect to that port. This is like your PC giving the server a phone number to call your computer at. Sometimes this causes difficulty with your firewall.

In passive FTP, your PC asks the server to pick a port, and then connects to the server on that port. This is like your PC asking at what phone number it can call the server. Since your PC makes the call, firewalls usally allows it.