An automatic or self-winding mechanical wristwatch is a marvel of micro engineering. At the heart of this type of watch is the automatic movement that collects the energy of your arm moving and uses this energy to keep the movement wound up. For a detailed description of an automatic movement and its history see HERE.
To illustrate the mechanical complexity of an automatic watch here is a detailed image showing the main component parts of a Sellita SW240 automatic movement.
Image copyright Sellita