On the ground it serves multiple purposes.
One purpose is to prevent your gravel from sinking into the earth when you walk on it. Over time, rain and gravity can push/pull your gravel quite deep into the soil, I think half an inch a year on walking paths can be expected, half of that on undisturbed locations. After some 10-15 years or so, depending on your climate and disturbance, most gravel will have sunk to ground level. Or the soil has crept up, depending on how you look at it.
Another purpose is to prevent seeds from weeds and whatnot from entering the soil, but then again, we all know how good inorganic soils can work. After a couple years on the fabric, compost will start occurring in your gravel and weeds will take hold. Earthworms will find their way around it no matter what. They'll be in there within a week or so.
Given that the fabric stops your gravel from sinking in, another advantage is that when you decide you want your gravel scooped out, you don't have to remove those couple of inches of top soil with it if you use fabric.
From what I've seen, the fabric can help soils stay moist for longer. But when unprotected it also can get pretty hot and cause more evaporation.
Due to the pressure of the gravel weighing more than air, you can expect some minor soil compaction below the fabric.
Fungi will grow through it, by the way.