What is Dynamic Range Mapping?

Dynamic Range Mapping is a more proper term for "tone-mapping" used by other HDR products. The term describes the same technique of mapping one dynamic range (in image) to another dynamic range (output device, such as computer monitor).

The primary difference between Dynamic Range Mapping and Tone Mapping comes from the underlying color model. Traditional HDR imaging applications are typically based on the RGB model, and this is why the tone-mapping technique is referred to as "mapping of tones" — that is the R, G and B tones. But HDR Expose is built on the Beyond RGB™ color model, which separates brightness (luminance) information in image from color (chromaticity) information. Therefore HDR Expose can use mapping in only one brightness channel without affecting color channels.

In HDR Expose and 32 Float, the Dynamic Range Mapping refers to 2 things:
First, it is the name of a one-click operation that maps the dynamic range of your picture into the dynamic range of your monitor automatically once you designate a mid-tone point (typically a subject of greatest importance in your image).
Second, and more generally Dynamic Range Mapping refers to manual adjustments that you can make using Brightness channel operations (Brightness/Contrast and Shadow/Highlight). With manual DRM you have much greater control over the choices that need to be made for your images.