The British wanted control of the Hudson River. This would help them block off the New England colonies from the rest of the colonies.
Winter At Valley Forge
The major reason this battle was fought was to convince soldiers with expiring enlistments to rejoin the army, and to also end the year on a positive note.
Battle of Cowpens/Guilford Courthouse
When American troops failed to invade Canada, a surplus of British troops was left. These troops decided to attack the Americans.
The Battle/Siege of Yorktown
The British were going to stay in Philadelphia for the winter, so George Washington decided to station soldiers at Valley Forge to keep an eye on the British.
During the battle, Lieutenant Colonel John Howard ordered some of his men to turn sideways for the oncoming British. This order was misunderstood, and the soldiers began to retreat. Thinking they had won, the British charged after them, but the Americans had already regrouped to attack them once again.
Cornwallis had his troops stationed in Yorktown. George Washington decided he wanted it back.