HPDE are High Performance Driving Events/School....Basically you go to a real race track and for the day/weekend you get an instructor in the car with you at all times really teaching you the finer points of driving your car at the limits in a safe controled environment. Eventually you get to the point where you can go solo and have fun. There's no timing, just driving and learning. I highly recommend them as you'll learn more about your car at these events that you'll ever learn auto x'ing or dragging the car. You get 20-30 minutes of non stop high speed driving 3-5 times a day.
It's quite addicting. I have a few vids of my sessions