"Stereo" here refers to the fact that you can look with both eyes and
make your observations with a sense of depth perception. This is indeed a step
up from a hand lens!
This technique allows you to examine the surface of the rock at higher magnification than the human eye can achieve on its own. Not that we would ever advise ignoring your very portable hand lens, but with a modern stereo microscope you get more flexible options for lighting and magnification, and in general, more relaxed observing conditions. Some stereo microscopes are equipped for both reflected light (like your hand lens) and also transmitted light. Transmitted light mode is particularly useful for observation of whole thin sections-- a range of low magnification that is not available from polarized light microscopes. The lowest magnification images used in this tutorial are comparable to what can be achieved using transmitted stereo microscopy, although the images displayed in the tutorial were made with a high-resolution transmitted-light scanner.
For making images of entire thin sections,
scanners such as this surpass transmitted stereo microscopy in several respects:
uniform focus across the entire section being the main advantage. Cross-polar
observation can be obtained by sandwiching the thin section between sheets of
properly oriented polarizing film.