In essence Blu-ray is a disk that is the exact same physical size as DVD but that can contain more then 5x the content. The mmost important thing to know is that every BD (short for Blu-ray Disk) player can play DVDs but that you need a BD player to play BDs.

More technical:

in order to do HD properly (that has roughly 6x the detail) something that could hold more and spit it out faster was needed. BD uses a blue laser instead of a red one for DVD and infrared for CD as well as having the data layer much closer to the surface (.1mm for BD, .6mm for DVD and 1.2mm for CD) a BD can hold 25GB on a single layer disk and 50GB on a dual. A BD also has a faster data rate 54mbps. When the BD movie format was created they also made some other improvements, they added two newer video CODECs (VC-1 and AVC to DVDs MPEG-2 that are more efficient) and they also added more audio formats including LPCM that is the original digital sound used to get the DD and DTS as well as DTHD (Dolby True HD) and DTS HD MA (Master Audio) that are lossless compressions. They also added BD-J so that studios can use cooler menus.

In conclusion: in essence a BD is a movie disk like the DVD but the movies on them have better pictures, better sounds and sometimes better menus.