According to the 3rd edition of the Glossary of Geology, convection has 4 different meanings. The definitions for economic geology, meteorology, oceanography and tectonics are slightly different however the underlying idea is the mass movement of something caused by a change in heat or density.
Convection currents are the driving force of tectonic movement.
Convection is the movement of the heat in the Earth. Convection causes the tectonic plates to shift. When they move we get tectonic activity and this causes a bunch of things to happen. Earthquakes, volcanoes, expanding oceans, mountain building. You name it, tectonics probably has a hand in it.
Convection is also found as a force in stars. To think about this concept we will use the closest start to Earth for studying...
Just like the earth the sun is made of different layers. We've all heard about the Earth's core (or seen the terrible movie called Core. Now that we've talked about geodes that movie makes less sense.) but we don't often chat about the core of the Sun. The sun is very important to life on Earth. We are at the perfect distance for heat to sustain life and with our magnetosphere blocking UV waves we get pretty auroras.
How exactly does convection work in the sun? Well, in the layer of the sun called the photosphere, convection occurs and moves the heat from the core. The photosphere is the lower layer of the sun's atmosphere and is where the brightness of the sun comes from. The core is where nuclear fusion takes place, this fusion causes enormous amounts of heat. This heat circles through the photosphere through convection currents.
It's simply amazing how much heat can do. It keeps our Earth moving and keeps sediments occurring. A professor at our schools likes to say "Without tectonics there would be no serious sedimentation." And this includes ocean currents, waves, rivers and all other forms of sedimentation.
Now, how cool is that?