Why did the 13 Colonies win the war for independence?

One major reason was logistics. While the colonies did not possess much in the way of material with which to make war, they had their materials available. Britain, on the other hand, had to wait for reinforcements and supplies to come from Europe. The British navy was the strongest in the world at that time, but it still could not compensate for the time it took to move men and supplies across the Atlantic Ocean.
Another major reason that the colonists won was foreign support. The French, Spanish, and Dutch joined the war against Britain. While these countries were not necessarily in favor of the colonial cause, they all viewed Britain as a rival, and this was a good excuse to go to war and try to steal British possessions. The addition of the French to the Revolutionary War made a localized conflict into a global one. Britain also had to be ready for the possibility of an invasion.
Another major reason that the colonists won was morale. By the time of Cornwallis's defeat at Yorktown, many in Britain had already grown tired of the war. The colonists, on the other hand, were only becoming stronger in their resolve for independence. This was part of the colonial strategy—to avoid any battle which would lead to the army's destruction while hoping that Britain would grow tired of fighting.