The Flight Director is a computer that calculates steering commands so you (flying manually), or the autopilot can more easily intercept or maintain selected flight parameters.
For example: you want to fly an ILS approach and have selected the appropriate frequency. You select the ILS mode of your flight director, and in addition to the standard 'raw data', positional glide slope and localizer displays, you get another set of needles or bars that give you pitch and bank steering commands to intercept and maintain that gs or loc.
The flight director computer creates it's input to the autopilot or display for hand flying by taking distance, speed, rate of change, and aircraft limitations to do things like: calculate an intercept angle to a course, show you when and how much to pitch or bank in intercept and maintain that course, change altitude, hold altitude, follow a glide slope etc. It will give you an appropriate corrections for the degree of deviation from the selected flight parameter.
All flight directors are not the same, a flight director on a new 737 covers a very comprehensive set of flight parameters; the T-38 flight director covers only a few parameters but they are very helpful ones. It will give you a 'steer' bar command to help you fly to and maintain a selected heading, it will help you maintain a localizer course or glidepath for a glideslope. None of those are necessary for very precise instrument flight procedures, but they are very helpful when they work.
