Blu-ray Disc (or BD) is an optical disc storage medium just as DVDs and CDs are but it is capable of much higher capacities of 50GB and more.
BD utilises a blue laser (which is actually violet) which uses a much shorter wavelength which is why it can store so much more than DVD.
Optical discs store information with the use of pits and lands which are lined up in a long spiralling track which starts near the centre of the disc and travels outwards. With BD, the pits are smaller, V-shaped and closer together. This allows for more to be fitted onto the disc.
BD-R: disc can be written once.
BD-RE: Can rewritable discs. (Re-recordable) and writing / remove the disc similar to DVD-RW and CD-RW BD-RE by using substances that change the status of tiered storage. When this is shot with a laser to change the status of the material back and forth a thousand times.