What is the theory that explains the movement of Earth's lithosphere?

The theory that explains the movement of Earth's lithosphere is plate tectonics.

Plate tectonics holds that Earth's rigid lithosphere is broken into large tectonic plates that move over the softer asthenosphere beneath them. Their interactions produce divergent, convergent, and transform boundaries, creating features such as mid-ocean ridges, trenches, mountain ranges, volcanoes, and earthquake zones.

The modern theory grew from Alfred Wegener's 1912 proposal of continental drift. Wegener presented evidence such as matching coastlines, fossils, and rock formations, but could not explain a convincing driving mechanism. Evidence for seafloor spreading and magnetic striping in the 1950s and 1960s supplied the missing support, leading to broad acceptance of plate tectonics.

A common mix-up is treating continental drift or seafloor spreading as synonyms for the full theory. Continental drift describes the movement of continents, while seafloor spreading is one process that creates new oceanic crust. Plate tectonics unifies those ideas and explains the movement of the entire lithosphere.