[burmanm]

It's not just how bright it can get, but also how specular highlights are retained. Instead of having a white blob of white blob, a screen with high peak brightness can show details in that white blob.

For example, clouds could be just white (low max brightness) vs. clouds could have details (high peak brightness). And this is especially important in how the HDR movie is graded (and which peak brightness it is targetting).

Vincent (HDTVTest) made a good video on the subject.