What is a Hot Spot?
Mantle plumes are areas of hot, upwelling mantle. A hot spot develops above the plume. Magma generated by the hot spot rises through the rigid plates of the lithosphere and produces active volcanoes at the Earth's surface. As oceanic volcanoes move away from the hot spot, they cool and subside, producing older islands, atolls, and seamounts. As continental volcanoes move away from the hot spot, they cool, subside, and become extinct.
Hot spots are places within the mantle where rocks melt to generate magma. The presence of a hot spot is inferred by anomalous volcanism (i.e. not at a plate boundary), such as the Hawaiian volcanoes within the Pacific Plate. The Hawaiian hot spot has been active at least 70 million years, producing a volcanic chain that extends 3,750 miles (6,000 km) across the northwest Pacific Ocean. Hot spots also develop beneath continents. The Yellowstone hot spot has been active at least 15 million years, producing a chain of calderas and volcanic features along the Snake River Plain that extends 400 miles (650 km) westward from northwest Wyoming to the Idaho-Oregon border.
However, keep in mind these are just theories. Nobody really knows the answer. The honest answer is that lots of folks are working on it but haven't come up with the answer yet.
Graphic After Morgan, J., 1971, Convection plumes in the lower mantle: Nature, v. 230, p. 42-43.