The Arlington House is an attraction-within-an-attraction. It was built by George Washington's descendants and was Robert E. Lee's house until the Civil War, when it was taken by the Federal Government to be used as Arlington National Cemetery. Thus, there is a lot of history here.
The house itself has an impressive facade, and provides a magnificent hilltop view of Washington, DC. It is easy to see why this site was selected.
They only let in 12 people at a time to limit the load on the second floor of the house, so you might have to wait a while to get in. While you are waiting, though, park rangers go through the entire history of the house and the Washington and Lee family trees (basically, Robert E. Lee married Martha Washington's great-granddaughter).
The house is furnished with many items that belonged to George Washington, Robert E. Lee and their relatives. It is large, though not especially lavish. There was limited access to the house for a while due to renovations, but you can now see both wings of the house and the basement, first floor and second floor (the attic is still closed to the public). There are also gardens and out-buildings that served as slave quarters, and a very small museum (one room) about the life of Robert E. Lee.
It's definitely worth seeing while you are at Arlington National Cemetery, but if you have seen other colonial estates and are short on time, it's probably not worth waiting a long time just to get into the house (you can see everything except the interior of the house without waiting).