On Earth, large rigid crustal plates float on the plastic mantle. It is thought that convection currents in the mantle cause these plates to move over the surface of the planet relative to each other. This causes continental drift, mid ocean ridges, rift valleys, oceanic trenches, mountain building, Volcanoes, and Earth Quakes.
Mars does not seem to have undergone as extensive tectonic activity as Earth. However, it is thought that there was tectonic activity for a short time, early in Mars' geologic history.
Some have argued that Valles Marineris is a Rift Valley caused by two plates splitting apart.
As Mars has cooled, the mantle has become less mobile, and no plate tectonics is currently thought to be active. It is thought that the water in Earth's oceans enters the mantle thru oceanic subduction zones, and this water helps to 'lubricate' the mantle flow on Earth. (This is unlikely to take place on Mars, which makes plate tectonics even less likely.)