No, you cant play a blu-ray in a regular DVD player. You CAN watch a DVD in a blu-ray player tho. They are equipped with both red and blue lasers.
The reason its called a blu-ray player is because it literally uses a blue laser to read the info on the disc. The reason for this is because a blue laser has a shorter wave length then a red laser and there for, more data can be squeezed onto the disc. Thus making it possible to fit HD video and audio on a DVD sized disc.
Think of the lines/grooves on an old record. It uses a diamond tip to play the music. If you used a pebble to try and play the record, its not going to work. Same thing with a blu-ray disc, the red laser that reads DVDs is too big and can not read the fine "grooves" (or dips and saddles they are usually referred to) of a blu-ray disc.