Aren't all Watches Automatic Watches?
No! Not all watches are automatic watches. Automatic watches are a subset of the set of mechanical watches. Also known as self-winding watches, automatic watches… well, they do just that - wind themselves. They're engineered so that energy provided by the natural motion of the wearer's arm is captured and used to wind the mainspring.
How Automatic Watches are even possible? Solar Power makes sense, but Arm Power?
With the right engineering, arm power really is all it takes to keep a mechanical watch wound and running. Automatic watches have an extra component that pivots back and forth in response to the normal, everyday motion of the wearer's arm. The pivoting weight within the watch is what "catches" the kinetic energy of the swinging arm. Since the pivoting weight is part of the system of gears and springs that make up the movement of automatic watches, it can connected to the mainspring and used to actually wind it.
Since the mainsprings of automatic watches, like those of normal watches, store energy (in this case, often enough for two days of operation), the watches continue to run even while the owner sleeps and the charging weight remains stationary. This stored energy is also the saving grace in case the owner doesn't move around enough in the course of the day to generate a full charge.
Back to the Future with an Automatic Watch
The concept sounds rather futuristic - afterall, automatic watches only need to be worn in order to keep running, despite being mechanical in nature, while "modern" digital watches will eventually stop working just because their batteries die. But first automatic watches were actually designed and built centuries ago. A self-winding pocket watch was created in Switzerland in 1770 - the wearer needed to walk around for a mere 15 minutes a day in order to keep it wound and running. That's a target timeframe that's still appropriate for today's automobile-obsessed lifestyle.
The early automatic watches, while inspiring, weren't as reliable as those we're used to today. Part of this was due to the fact that they were pocket watches, and thus not exposed to as much movement as a wristwatch. After the First World War, though, sales of wristwatches took off and automatic watches based on the wristwatch paradigm, with greater available kinetic energy, soon took off. After that, it just took Rolex (who else) to increase the winding efficiency and the amount of time that the mainspring could power the watch without motion on the part of the wearer, and the fully reliable, fully-automatic watches that exist today were born. Most of the mechanical wristwatches on the market today are automatic - it's too much of an advantage to do without in most cases, though some exclusive brands make manual-only watches, preferring the slim elegance that's not possible to achieve in automatic watches because of the added thickness.