What Elsinore said.
A great example is this image (taken by chakalakasp in the original HDR contest).
Without HDR, you would either end up with the windows being overexposed (showing none of the detail) if you have the expose for the inside correct or the inside would be underexposed for the window detail still to be there. The HDR process makes it so none of either the inside or the window details will be lost by combining the images with separate parts at correct exposure.
This can also apply to a scene where you are looking out a bright window at your place through a room. You would have to deal with either underexposing the room or overexposing what is outside without HDR.
