With HDR images, each pixel isn't only represented by R G and B values ranging from 0 to 255, there's also a fourth value that stores light intensity and is a limitless float value (eg 0.48737838).
So while in a normal 'Low Dynamic Range Image' like a jpeg file, the sun may have pixels that are 255,255,255, (bright white) and a persons shoe may have a pixel that's 0,15,108, (dark blueish), the most brightness difference they can have is 255. Get it? Pure light is only 255 time brighter than pure darkness.
But with a HDR image the 'light intensity' value of a shoe pixel could be 0.0000000557 and the 'light intensity' value of the sun could be 78783934.995.
So basically, there is a very high range of intensity in a hdr image.
I hope that made sense.