How does a sailboat sail

Skillful sailors know just how to tack into the wind, but the physics of what makes the technique work is complex.
A key factor is the pressure differential that forms across the sail.
With the boat angled into the wind, the airstream splits around the sail; the outward-arching downward side of the sail creates a longer path for the wind, which rushes over it more quickly than it does on the concave side.
The faster air forms a low-pressure area, so the higher-pressure air on the sail's concave side pushes into it, essentially changing direction.
The boat would simply be nudged downwind if not for the keel, which hangs down in the water like a wing.
Downwind motion of the boat across the water causes the water to flow faster around one side of the keel than the other in a pattern opposite that of the air flowing around the sail.
The resultant pressure differential causes the water to push against the keel, balancing the direction of the sail force.