what are mantle convections and plate tectonics?

In simple terms:

The earth's crust (technically, it's lithosphere) is divided up into numerous large pieces, that fit together like jigsaw puzzle pieces. These crustal slabs are called tectonic plates.

The plates are not stationary: they move about, very slowly and imperceptably. For example, North America is receding from Europe at a rate of about 2 cm per year: about the rate at which fingernails grow.

These 2 continents are receding from one another because of the mid-Atlantic ridge. This is a divergent plate boundary, meaning that the plate diverge - move away from one another. The "gap" left by the two plates moving apart is filled in by magma welling up from below.

At other places, called convergent boundaries, tectonic plates collide. If one is made of oceanic crust and the other from continental crust, the plate made of oceanic crust sinks below the continental crust: this is called subduction. The subducted crust melts.

Mantle convections are directional flows of the mantle. As mantle nearer the core heats up, it become less dense and starts rising. On the other hand, mantle that has been farther away from the core for long periods of time is cooler and denser, and so sinks. So there is a constant - but ever so slow - turnover as regions of mantle rise and other regions sink.