"Clean coal" is a plan to remove all carbon dioxide from the mining, transportation and burning of coal in industry and electricity generating power stations. The goal is to pump this CO2 deep under the ground into old gas and water deposits, where it will be trapped forever. So the coal will be "clean" and "green".
There are various small-scale trials going on around the world. Scientists and Governments are desperately hoping that they can make this work, and work cheaply, to take advantage of the vast amounts of coal that still exist on the planet.
The alternative, which many think is a better idea, is to spend the money on research and development of other non-polluting and renewable sources of energy, eg, solar, wind, water and geothermal.
More information on the Wikipedia page