Active displays have a little transistor built into the display for each pixel. This means the thing is definately on or off. A passive display doesn't have this so you end up with nearby pixels turning on partially. This gives you a really smeary screen and if you've ever seen old LCDs the window lines problem. The edges of a window continue the full length of the display and have a funny ghost image look.

The response time for an active display is much better than a passive display as well.