Volcanism.

What is a volcano?

A volcano is simply a point where magma reaches the surface — but where and how that happens varies a lot, and it directly determines both the type of volcano that forms and the type of igneous rock it produces.

Volcanoes form in three tectonic settings

At subduction zones

where a subducting oceanic plate melts as it's forced deep underground, that melted material rises through the overriding plate and erupts above it. This is the source of most of the world's most recognizable, explosive volcanoes: the Cascades, the Andes, the entire "Ring of Fire" around the Pacific Ocean.

At divergent boundaries

where plates pull apart, magma rises to fill the gap and erupts relatively gently and continuously. Most of this happens invisibly along mid-ocean ridges on the sea floor, but it's visible on land in places like Iceland, which sits directly on a divergent boundary (the Mid-Atlantic Ridge).

At hotspots

a small number of volcanoes aren't at plate boundaries at all. Instead, they sit above a stationary plume of unusually hot material rising from deep in the mantle, which melts through the crust above it regardless of what plate boundary activity is happening nearby. As the plate slowly drifts over the stationary hotspot, it leaves behind a trail of volcanoes — this is exactly how the Hawaiian Island chain formed, each island progressively older the further it sits from the currently active hotspot.

The type of volcano that forms depends heavily on how thick (viscous) the magma is, which in turn comes down to its chemistry

the same basalt/andesite/rhyolite spectrum covered on the Igneous Rocks page:

Shield volcanoes

form from low-viscosity, basaltic magma that flows easily and spreads out over a wide area before solidifying, building a broad, gently-sloped dome shape rather than a steep peak. Eruptions tend to be relatively gentle (effusive) rather than explosive, since low-viscosity magma lets gas escape easily instead of building up pressure. Hawaii's volcanoes are the classic example.

Stratovolcanoes (composite volcanoes)

form from higher-viscosity andesitic or rhyolitic magma, which doesn't flow easily and traps gas — building pressure that releases in more violent, explosive eruptions. The erupted material (both lava and ash/debris) piles up close to the vent, building the classic tall, steep-sided, symmetrical cone most people picture when they think "volcano." Mount St. Helens, Mount Fuji, and Mount Rainier are stratovolcanoes, and this is also the type most associated with subduction zones.

Cinder cone volcanoes

are the smallest and simplest type — built from a single, relatively short eruptive episode that ejects small fragments of cooling lava (cinders) into the air, which fall and pile up around the vent into a small, steep, cone-shaped hill. Many cinder cones only erupt once in their lifetime.

The connection back to rock

basaltic (low-viscosity) magma builds shield volcanoes and produces basalt; andesitic/rhyolitic (high-viscosity) magma builds stratovolcanoes and produces andesite or rhyolite (or obsidian and pumice, in especially violent, fast-cooled eruptions). The type of volcano you're looking at is really just a visible record of the chemistry of the magma that built it.