Cameras with more dynamic range allow you to take photos with dramatic differences in highlight and shadow areas while retaining detail in both.
Think of a brilliant sunset on a rocky beach: Bright sunset in the background, with dark rocks in the foreground. High dynamic range means more of the extremes will be faithfully reproduced.
Dynamic range test data courtesy of DxO Mark.D810 test data on DxO Mark 1DX test data on DxO Mark
Handles even better than its predecessors; Absolutely spectacular images from the 36-megapixel image sensor; Unusually wide sensitivity range for its resolution; Improved performance and buffer depths; Improved video feature set; Impressive low-light autofocus
Prone to moire and false color with some subjects; No longer available with a low-pass filter; Demands excellent lenses for the best detail; White balance tends warm under tungsten lighting