Yellowstone is a supervolcano caused by a Hot spot or mantle plume underneath the American continent. Most continental crust is 20 to 30 miles thick, here it is just 2 caused by the rising of a plume of hot mantle underneath the crust. As the North American plate has moved over the Hot spot it has punched holes through the continental crust. Unlike Hawaii the crust here allows sporadic violent eruptions 100,000s years apart although some quieter eruptions of lava have occured.
The volcano has had 3 major eruptions in the past 2 miilion years and averages an eruption every 600,000 years or so. The last eruption around 660 000 years ago devastated 1000 sq miles and ejected 240 cubic miles of material. The caldera from this eruption is 85km by 45 km and is 1km deep - in fact so big you don't know you are in it! The caldera was gradually filled in after the last eruption by rhyolite lava flows which only stopped 75,000 years ago.