With access to the RAW pixel information they can artificially under- and over-exposure then map those into an HDR image.

Your screen (and popular image formats) are 8-bits per color channel. Modern digital sensors can do 12-14 bits of useful data per color channel typically (16 for the really high end stuff).

To even save or display the image from these sensors you'd have to compress the 12/14-bit color range into 8-bit anyways. Single-image HDR is simply the ability to tweak this transform to your benefit.