The premise of an automatic watch movement is that a rotor (shaped like a half circle) spins in the catch case, which in turn winds the main spring. The rotor is connected at what would have been the center of a full circle, and gravity weighs it down such that it spins when the watch is moved around. Typically, if you wear a watch daily, you should never have to worry about it stopping. This is because it moves around enough to sufficiently wind.
However, when you start to have more than one watch, especially multiple automatics, you can get into an attention problem. All these movements needing to be constantly wound. There are only so many watches you can have in a day. Most watch owners will spend a good amount of time each day manually winding watches. This does not mean spinning them around in your hand, but most, if not all automatics can be manually wound from the crown, just as a manually wound watch. This can become a chore, unless you really want to sit and remember to wind watches each day.
The job becomes easier if you have a power reserve indicator on your watch. This is a simple readout which, more or less, indicates how tightly the main spring which powers your watch is wound. The bottom line is that as your watch collection grows, you need to spend more time making sure that they are wound. So why not just wind a watch when you wish to wear it? That is a good question actually, because some people might want to preserve the life of a watch by not winding it all the time. Main springs are usually very hardy and will not lose their particular tensions. However with more vintage or expensive watches you might want to wind them only when wearing them. Some watches have very complex movements that provide full calendars, moon phases, and other information. One you let the watch wind down, you need to reset all that information which can be tedious and require looking online (for example with the moon phase indicator). Because of this, it is important for watches to be ready to go when you want to wear them, and for accuracy's sake.
What a watch winder does it spin on its axis and angled in a slightly diagonal manner. Most of them do not spin all the time, and will rest for a few hours before spinning again. Most are powered by a wall socket, others have the power of being battery operated for travel purposes. Of course because there is a motor in the winder, there is a concern about them making noise. However, even the two very inexpensive watch winders I own are relatively quiet and would not wake you up at night.
There will be only articles in the near future providing more detail on choosing or finding a watch winder. Specific questions can be answered as well if left in comment form. However, you need to realize that watch winder for the most part, are exorbitantly expensive for what you get. Most are European designed and manufactured in the highest quality. Yes of course they are meant to house your "precious" timepieces, but they priced like any other luxury good. For example a single watch winder be a few hundred dollars, while multiple watch winders are often in the several if not many thousands of dollars. While these are often very nice "watch appliances," they provide little to no feeling of value.
A new stream of Chinese made watch winders are coming into the United States being priced very well. Often no more than about $200. I purchased two double watch winders of eBay for about $50 each (one brand to look for is Garinin). This is not exactly bargain basement pricing, but it is a worthy investment once you start owning several automatic watches. Of you have hand-wound manual watches, there are still some options out there, but hand-wound watch winders are complex and always expensive.
The Chinese watch winders are usually on eBay or some other distributor websites. I plan on discussing how to find these another time.