This question refers to the time after the Revolutionary War and before the War of 1812. During this time, the British kept forts on American territory in what was then called the Northwest. From these forts, the British gave aid to Native American groups that were opposed to the United States.
The British maintained these forts because they wanted to hold on to as much power and control as they could in North America. They still controlled Canada which was adjacent to the American Northwest. If they could keep a foothold in American territory, they might be able to limit American power. Furthermore, the British kept the forts because they could. At that point, the Americans were not strong enough to oust them from forts in such relatively remote locations.
One reason the forts were in a strong position was because they were located in the lands of Native Americans who were friendly to the British and opposed to the United States. These Indians were allied with the British because they thought the British would help them against the Americans. They felt that the Americans were more interested in expanding into Indian land and were, therefore, more of a danger to them. If they allied with the British, they would have a powerful friend who, they thought, could help them resist American expansion.