RepRap is short for Replicating Rapid-prototyper. It is a practical self-copying 3D printer - a self-replicating machine.
A 3D printer builds parts up in layers of plastic - this technology already exists, but the cheapest commercial machine costs about €30,000 - and it isn't even designed so that it can make itself.
The RepRap team is developing and giving away the designs for a much cheaper machine with the novel capability of being able to self-copy (material costs are about €500). That way it's accessible to small communities in the developing world as well as individuals in the developed world.