The north wind and the sun both aim for the same thing: to show that they are strong, but they go about this in different ways, as illustrated in their contest to remove the coat from a traveller going down the road.
The wind blows as strongly as it can, to try and tear the coat off by brute force, but the traveller resists this, and only wraps his coat more tightly around himself. Then it is the turn of the sun:
Then the sun came out from behind a cloud and began to shine down upon the traveller with his power. The traveller felt the sun's genial warmth, and as he grew warmer and warmer he began to loosen his coat. Finally, he was forced to take it off altogether.
The sun, then, succeeds where the wind had failed, by exerting gentle pressure, 'genial warmth' rather than a show of brute strength. The sun is more subtle and persuasive than the wind, which relies on sheer power. By being more gentle and patient, the sun is also more effective. The moral is that persuasion is better than force.
This particular Aesop's fable is somewhat unusual in that it features personified forces of nature rather than animals, but its moral is probably one of the best-known.