What is plate tectonics?
The theory that the Earth's outer shell is divided into rigid plates that move relative to one another over a weaker layer beneath — explaining earthquakes, volcanoes, mountain ranges and the distribution of fossils with a single mechanism.
The structure involved. The lithosphere — crust plus the rigid uppermost mantle — is broken into around a dozen major plates and many smaller ones. Beneath it the asthenosphere is hotter and behaves plastically over geological time, allowing the plates above to move at rates of a few centimetres a year, comparable to fingernail growth.
The three boundary types, which explain almost everything:
Divergent. Plates move apart, and new crust forms as magma rises. Mid-ocean ridges are the main example, and seafloor spreading there was the observation that confirmed the theory.
Convergent. Plates move together. Where oceanic crust meets continental, the denser oceanic plate is subducted beneath — producing deep trenches, the deepest earthquakes, and volcanic arcs from melting above the descending slab. Where two continental plates converge, neither subducts readily and the crust thickens and buckles, which is how the Himalayas formed and are still rising.
Transform. Plates slide past each other, producing earthquakes without volcanism — the San Andreas fault being the standard example.
How it was established. Alfred Wegener proposed continental drift in 1912, citing the fit of coastlines, matching fossils and rock formations across oceans, and palaeoclimate evidence. It was largely rejected for decades because he could not propose a plausible mechanism, and geologists reasonably declined to accept continents ploughing through solid ocean floor.
The evidence that settled it came in the 1950s and 60s: mapping of mid-ocean ridges; magnetic striping on the seafloor, where symmetrical bands of alternating magnetic polarity either side of a ridge recorded reversals of Earth's magnetic field as new crust formed and spread; the age of ocean floor increasing with distance from ridges; and earthquake distributions tracing plate boundaries precisely.
This is a good illustration of how science works — a correct idea rejected for a legitimate reason, then accepted when the mechanism was found.
What drives it involves mantle convection, ridge push and — probably dominantly — slab pull from subducting plates.