I was unable to find this in any previous thread but apologies if it has been dealt with. I have recently been reading up on the US war of independence, a topic I had really read much about since college and I'm really curious to know why the surrender at Yorktown was so consequential. Given that the British still had a sizable fleet and an army in the colonies, why did this defeat spell the end? One of the authors I read (Middlekauf) even cites Lord Norths response to the surrender as indicating that it was all over. What about that victory made them think this was true?
Your confusion is understandable, as the surrender at Yorktown represented only a fraction of British troops in America. 8,000 British troops surrendered, out of ~40,000 on the continent. The prevailing British wisdom prior to the war had been that with a few victories over key cities, revolutionaries would abandon the cause and return as loyalists. Hence the original strategy of offering pardons to anyone who would abandon the revolution. After the defeat at New York, Washington came to realize that the war was not about gaining and holding territory, but about attrition. It didn't matter if the British held the cities if they were unable to destroy the Continental Army in the field. Washington altered his strategy accordingly, avoiding major engagements while attacking targets of opportunity (like Trenton). Staying inland also neutralized the main British advantage, naval power. This strategy, combined with General Gates victory at Saratoga resulted in the end of major British combat operations in the North, and the pivot to a Southern strategy. (At this point, the British still controlled New York, as they would until the end of the war). As Saratoga proved that the British would not be able to easily subjugate the northern colonies, Yorktown proved the same in the south. Colonial victories had repeatedly proven that there would be no great loyalist '5th Column' that would rise up to support the British, and proved that the war was probably unwinnable with current troop levels.
In this way, the choice by the British to recognize American independence was as much a financial decision as a political one. They could have continued to fund an American campaign, but it was rapidly becoming clear to financiers in Parliament that such campaigns would require significant further investment, and were unlikely to produce any better results. At that point they concluded that it was time to cut their losses, rather than continue a war that could become financially ruinous to the Empire.
Edit: I forgot this detail: Washington did not view Yorktown as the end of the war at the time. After the battle, he expected the war to continue, and returned to planning for an attack against the British in New York.
Main Source (other than those above)
Washington, a Life by Ron Chernow (as part of my continued effort to cite this book for all my answers)
John Adams by David McCullough