Chris and Lump,
A Flight Director is a device that shows in your ADI (Attitude Director Indicator, or "artificial horizon") which attitude & heading you should follow.
In an ILS procedure, for instance, it will show how do you need to fly in order to stay on localizer and on glide slope. So, in a few words, the Flight Director directs your flight (simple this way!).
Roughly, in modern acft the FD replicates what the autopilot is doing. In older ones (like the 737-200, Sperry SP-77 autopilot), the FD and the AP are completely separate systems - and you need to place the same command twice: one for the autopilot, another for the Flight Director in order to check in your ADI if the acft is following what you intended to do.
I hope this simple, not very accurate explanation helps you.
Best regards,
Pif Paf