Gears come in all shapes and sizes. They are the toothy wonders that make the world go around, and they're incredibly important in the operation of a motor vehicle. There's a more specific type of gear that allows your automatic gearbox to operate. It's called the planetary gear set and the way it works will have your head swimming in concentric circles. That is, until you watch this wonderful classic video that provides a clear view of their operation.
A planetary gear set is comprised of an outer gear ring that's called the ring gear. Inside, you have a sun gear that has a fixed point in the center and a planet gear (or gears) that rotate about the sun gear. As they rotate inside of the ring gear, the planetary gears create pitch circles that can be formed into a gear train that, in turn, is hooked up to input and output shafts.
The input shaft will come from the engine and the output shaft will head to the driven wheels. By combining planetary gear sets, you're able to create a great a range of gear reductions. These reductions are necessary to get your vehicle rolling comfortably and efficiently, and they're where you'll find your various "gears," such as first, second, third, reverse, etc.
You create these gear ranges by combining the gear sets in different manners to create different output ratios. You'll need a higher ratio to get rolling in first gear. In this instance, both gear sets work together so your engine torque is multiplied and sent to the wheels. Once you're moving, one of the gear sets might be able to relax and let the other one do the work. This could switch when it's time to go to third gear.
By altering which gear sets are interacting with either the input, output, or both shafts, you'll have an automatic transmission that's making sure you're rolling down the road in the right gear.
All of this and more is described clearly in this cool black-and-white video. Give it a look, and you'll see you can learn from the past.