A mechanical watch simply takes a reserve of power, and releases that power into evenly timed increments.

Take a typical water faucet.  The knob can adjust from full on to barely a dribble.  If you adjust it to the minimum, you
can get the spout to release individual drips at a regular rate (that regular drip-drip of a leaky faucet is a good example).

If we take this analogy and translate it to a simple mechanical watch, the water source (power) is the wound mainspring,
and the balance is the control valve.  The balance is the wheel  that you see rapidly oscillating when you open the back of
a watch, incrementally releasing the power from the mainspring. From there a series of gears (power train) in between
the mainspring and the balance step down the speed, and run the hour, minute, and second hand.













For a good movie, created by the Hamilton Co. in 1949, see How a watch works on the Internet Archive project.
Great Wheel (or Mainspring Barrel)
Power Train (Balance Wheel not shown)
A (somewhat) simplified explanation of how a mechanical watch works: