Threading systems let multiple code paths run at the same time. Why would anyone want that? Simple: impatience. It's no fun waiting for the computer to finish one thing when you want it to be doing something else.
So what are "hybrid" threads and why does Parrot need them? Well, there are two common schools of thought in building threading systems for high level language runtimes. The Java people call them "green" threads and "native" threads. As with any design tradeoff the right answer is to cheat and just take all the good properties of both options.