While Yellowstone National Park is most well known for its geysers, it also has (perhaps surprisingly to some) a wide variety of landscapes that requires many days to explore. As the park layout and size can overwhelm the first time visitor, we'll be describing multiple drives for the park.
This drive is in the northwest corner of the park, from the north entrance at Gardiner to Madison. The first 5 miles follows an arid canyon up to Mammoth Hot Springs, which has a huge (mammoth?) display of hot springs and carbonate deposits (wikipedia says two tons of it are added every day). From Mammoth you climb to the scenic Yellowstone Plateau, and encounter hot springs and pools around Norris. At Norris you can turn to Canyon, or continue to Gibbon Falls and the junction with the east entrance road at Madison.
The national park web site has three maps with more detail: