Digital imaging is largely a linear process (parts of it anyway). So as the tonal values approach 255 (pure white) then can still have detail...but once they reach pure white, they just stack up and you get more and more pixels that are white (no detail).
This is represented in an image's histogram. if you have pixels that are 255 (as bright as they can get), the histogram stacks up and we say that you've 'clipped the highlights'.
So if you try to recover those highlights...there is nothing to recover (no detail). You can make the highlight darker, which would be taking all those pixels at 255 and making them darker. But you wouldn't be able to separate then into the detail (different tones) from the actual subject.
Now, when it comes to looking at the image and the histogram on the camera's LCD, you are not actually looking at the full potential of the image (if you are shooting RAW). The image and thus the histogram are a JPEG preview that is generated from the RAW. So if you take that Raw file into a Raw editing program (Adobe Camera Raw / Lightroom), you may find that you can recover some of the highlights that you thought were blown out.
So if they really are truly blown out...then no, you can't recover them. But if they only look blown out, you may be able to get something...but it depends. Does that make sense?