A React component is supposed to be a pure function, a mapping from props+context as input into an output which is a React element plus sideeffects (which when executed by the React library will often change the context). State lives in the context.

To illustrate statefulness: If you drop a flummy ball on the floor, it will bounce back and doesn't change. If you drop an egg, it will change and you can't drop it easily again. The ball is stateless, the egg is stateful.