That's a great question and I'm excited to answer it. :) A RepRap is a self replicating rapid prototyper. In other words, it's a 3D Printer which can make more 3D Printers and 3D Printers are like office printers except they can make plastic things like iPhone cases or whistles.
I love RepRap's because "in a way", they are living creatures. They use symbiosis to evolve and grow. Humans like RepRap's because they can print neat stuff and make RepRap's for their friends. RepRap's like humans because humans replicate and innovate them. It's a great relationship. :)
Most RepRap's use fused deposition modeling (FDM). FDM creates 3d parts by depositing a thin bead of molten plastic across a flat print area, one layer at a time. Watching a RepRap print is hypnotic.
You can become a part of this growing community of RepRap's and RepRapper's. You can build your own RepRap and a kit is a great way to get started.
To see the RepRap in action, watch this video: http://www.youtube.com/watch?v=HDtit728L70
To see how a RepRap is assembled, check out our assembly videos: Assembly Videos