Earth is geologically active because its internal heat keeps the outer core and lithosphere molten, encouraging plate movement and volcanic activity. Earth's crust consists of tectonic plates floating atop the malleable mantle, which in turn rises and falls over the semi-liquid outer core. The intense heat forces molten rock up toward the surface, creating new crust and driving intense geologic activity.
Earth's geological activity is due to its intense internal heat. The planet still retains heat leftover from its creation when a stellar bombardment rendered the young planet molten and intensely hot. Over time the outer surface of the planet cooled, but the interior remains hot in part due to the decay of radioactive elements in the core. This heat drives the planet's geologic activity and keeps its surface in constant motion.
Of the other terrestrial bodies in the solar system, the moon and Mercury lack geologic activity because, being small bodies, they cooled off relatively quickly, and their cores solidified. Mars cooled due to its thin atmosphere but more recently than the moon or Mercury. Venus is a geologically active planet due to the intense heat its atmosphere traps near its surface, but its surface does not consist of discrete plates, so it lacks some of the characteristics of Earth.