As mentioned, microwaves cook by a different process than regular ovens, so they can do it more quickly.
Regular ovens simply use hot coils to heat air in a closed chamber, and the hot air heats the food to cook it. This can take awhile though because air isn't a very good conductor and the hot air created only heats the outside of a food. The inside of the food gets heated because the molecules of the food closer to the outside of that food get hot and then transfer that heat to molecules of food next to them farther inside the food ("conduction"), and so on, all the way to the middle of the food which can take a while).
Microwave ovens don't heat the air inside their cavities (you can tell that because when you take a heated food out, the air isn't hot...maybe it's a bit warm from the steam coming out of the food though).
Microwaves penetrate/beam/radiate directly into the food instead, and as mentioned make certain kinds of molecules (like water and fat) vibrate, which creates friction, which creates heat.
Since the heating action doesn't have to move slowly from the outside in, it can more directly (and therefore quickly) cook the food.
That's a little simplified, but more or less right I think.
There's also the type of heat transfer called "convection." That term can get tricky when discussing regular ovens vs. microwave ovens since some microwave ovens these days also come with a convection mode (which can be used with the microwaves, or alone, or not at all). Actually that's really "forced convection," since plain old convection in the technical sense happens in a regular oven, but is usually just shortened to "convection" when not being technical.
Just be aware that microwaves can't "brown" things in the traditional sense and are blocked by metals...otherwise pretty much anything can be cooked in a microwave.