The primary reason Earth's tectonic plates move is that they float on convection currents in the mantle. These convection currents are caused by the heat from the Earth's interior, which creates a cycle of rising and sinking material in the mantle. As the mantle material heats up, it becomes less dense and rises, while cooler material sinks, creating a circular motion. This movement helps to drag the tectonic plates along the surface of the Earth.
So, the correct answer from your options is: they float on convection currents in the mantle.
The other options provided are not accurate explanations for the movement of tectonic plates. For instance, while gravity does play a role in helping to subduct plates, it is not the primary driver of their movement. Liquid iron in the outer core contributes to the Earth’s magnetic field and the geodynamo process, but it does not directly cause the movement of tectonic plates. Ocean currents near mid-ocean ridges do not push tectonic plates either.