laying stepping stones in gravel path
Sand is a material that is easily moved to get each stone at the proper level to the adjacent surfaces or stones. To set them directly on the gravel, would be difficult at best. When setting the stones on sand the stone is tapped in with a rubber mallet to essentially compact the sand. But am really getting the cart before the horse. 

Starting with the gravel, with things needing to be done as quickly as possible to follow the old adage "time is money", if you are a builder/contractor, machinery is brought in to cut the sub grade low enough to accept the gravel base. A lot of time is not needed for this since the gravel will help flatten out high and low places to get it within a reasonable working plane. A big advantage of the gravel is good drainage, and in colder climates some protection against the forces of freeze-thaw, worth doing it on those merits alone.

With the gravel in place, graded pretty flat and compacted, one thing needs to be added that was not mentioned in your post, a layer of filter cloth. This separates the sand from the gravel, other wise it will settle between the gravel and more or less become of no value to the support of the stones since water from rain, melting snow, cleaning will eventually wash the sand down through the gravel. 

Next the sand, this material is fine enough to move around with your hands, or trowels to "fine tune" the level of the stones. An inch is good to work in. I have set stones directly on the dirt before, and to have sand would have made the work much easier and faster, but for me sand costs. Working directly in dirt to get a good set, takes lots of time.

Depending on how tight you set the stones depends on what you can put between them, if they are set tight, you can do nothing or add sand between them. If they are set a few inches apart, you could use a small pea gravel to fill the gaps, a border would be good here to contain the easily moved pea gravel. You might could use grass in larger gaps, but the fast drainage under the stones would make it difficult to keep the grass watered well enough.