While this is a contentious subject, most researchers in the field would agree that "hotspot" volcanism results from the intersection of a plate with a mantle plume.  However some folks would like it to be driven by lithospheric cracking or edge driven convection.  Whether plumes originate from the core mantle boundary (CMB) or elsewhere in the mantle remains somewhat controversial. 

Plume generation requires a significant thermal boundary layer, and the only one we know of within the deep earth is the CMB.  Recently we have identified low shear wave velocity provinces (LSVPs) on the CMB, the edges of which have been shown to lie vertically below hotspots at the time of their eruption.  Leading to the hypothesis that the intersection of the LSVPs with the outer core and the lower mantle creates conditions favorable to plume generation.

For more info see:  Burke, K., Plate Tectonics, the Wilson Cycle, and Mantle Plumes: Geodynamics from the Top, Annual Review of Earth and Planetary Sciences, Vol. 39: 1-29, May 2011

Burke, K., Cannon, J., Plume-Plate Interaction, Canadian Journal of Earth Sciences, 2014, 51(3): 208-221, 10.1139/cjes-2013-0115

Hi John, Thank you for your answer to the question that I asked.  I will give you a thumbs up on your answer.. However, the model that you presented does not fit the Yellowstone hot spot that is characterized by explosive rhyotic ash.

Hi Paul,  The plume of hot mantle rocks "ponds" at the base of the lithosphere where it flows up into weak zones (rifts or sutures) where it can infiltrate the crust.  The mixing  between the deep mantle rocks and the crust creates the suite of magmas found at Yellowstone.   You chose one of the most contentious hotspots to focus on.  Yellowstone is one of the few that some people want to call an upper mantle plume. 

Hi John, Thanks very much for your answer. It is nice to know of  a different kind of hot spot.

Nice summary about the "plume debate" above Matt(John). Yellowstone is the end of a series of eruptions along the Snake River Plain (SRP), where both basaltic and rhyolitic material made it to the surface. The idea is that the basalt represents mantle melts that only slightly interacted with the crust, while the rhyolites are basally heated (think mantle melts below), evolving magma bodies (you can argue over whether or not the basalts physically interact with these as well). The volcanic centers along the SRP get older to the West, and this is where the link to age progressive hotspots comes in. A connection has been suggested to the Columbia River Basalt, a place where a large volume of basalt was erupted, potentially the plume head made it to the surface there. There's a whole literature on trying to geophysically "image" the mantle plume that should be feeding Yellowstone, if it is indeed a plume-driven hotspot.