Daniel Boone is really famous for one major accomplishment. His major accomplishment is that he spearheaded the exploration and settlement of what is now the State of Kentucky.
In 1767, Boone made his first trip into Kentucky on a hunting expedition. In 1773, he made a much more important trip to Kentucky. At that point, he brought his family and other settlers (a total of around 50 people) with him. They were the first British (America was not yet independent at that point) people to try to establish a settlement in Kentucky.
After the Revolution (in which Boone fought, mainly against Indians), Boone became one of the leading citizens of Kentucky. He held various positions in government in the new territory. During this time, he helped to settle Kentucky, doing things like helping to establish roads, survey land, etc.
This was Boone's major accomplishment--he did more than any other individual to settle and develop the area that is now Kentucky.