>All the answers, though somewhat corrrect, are not how it actually works.
I think the most concise way to explain how reverse thrust works is conservation of momentum.
Using a simple control volume around the engine, and integral momentum equations, you can calculate thrust as well as reverse thrust. But here's a tangible analogy, since I'll get yelled at for that..
Imagine being on a boat. Someone standing outside the front of the boat (fore) tosses you rocks very slowly. You throw the rocks back at him/her with a much higher velocity. Here, airflow is simplified to be many little rocks. The net difference in momentum is what creates a force backwards. To create thrust forward instead, just throw the rocks backwards with high velocity. The key to understanding the concepts behind propulsion is momentum, not drag.