The inner planets of the solar system are composed of rock. Small, cool planets, like the Moon and Mars, lose their heat by conduction. Convection is much more exciting. It powers the plate tectonics and other fancy styles of geology that the Earth and Venus have. Inside a star, conduction doesn't work because the molecules are too far from one another, so heat moves either by radiation or by convection.
Radiation operates where the gas of the star is transparent, as it is when it is especially hot.
Each of the little granules in Figure 4 marks a place where convection is gurgling up from below. Convection dredges up atoms manufactured in the core of the star. Astronomers like this because it gives them some idea what's happening deep within the star, where they can't see. Oh, Smoggy Day Not all hot fluids convect. A smoggy day in Los Angeles or any other big city illustrates what happens when things don't convect.