When we remove a tree, we cut it as low as the ground allows, usually a few inches. What's left is the stump and the root flare, and the question every homeowner asks is whether to pay to grind it. The answer depends on what you plan to do with the spot.
Grind it if you want to plant grass, put in a bed, run a fence, or pour anything there. A stump grinder chews the stump and the top of the root flare down eight to twelve inches below grade, we backfill with the chips and some topsoil, and within a season it's lawn. Grind it too if the tree died of a fungal disease like armillaria, since the rotting stump can host the fungus for years.
Skip it if the stump is in the woods, at the back of a large lot, or somewhere you'll never see it. A hardwood stump takes five to ten years to rot on its own, faster for maples and poplars, slower for oaks and locust. Some people cut them to a seat height and leave them. That's a perfectly good choice and it costs nothing.
What grinding doesn't do is remove the whole root system. The lateral roots stay in the ground and decompose over time. That's normal and it's not a problem for grass or most plantings. If you're building on the spot, that's a different job called stump removal, where the whole root ball is excavated, and it's what we do in land clearing.
We quote stump grinding as a separate line on every removal estimate so you can decide with the number in front of you. There's no wrong answer, just the one that fits your plans for the yard.