Here's the "geek" angle... Each color pixel is represented by three numbers (from 0 to 255)... one each for the red, green, and blue values. A pixel that has values of 0, 0, 0 is pure black, while a pixel with values of 255, 255, 255 is pure white. While a "pure" red pixel, would be 255, 0, 0.
A "blown out" pixel is a "pure white" pixel at 255, 255, 255. So why does this matter in digital photography? It doesn't look so good for one thing on your screen, but there's also a major problem with printing. A blown out pixel shows up as "nothing" on the printed paper... literally. In order to make "pure white" the printer will not deposit any ink on that area of the photo. A printer can't make "white", it relies on the color on the paper for "whiteness". If the area blown out is large enough, it will look like there is a "hole" in your image. There will be absolutely no details in that region.