Once we have removed a tree, the stump that remains is often ground out using a stump grinder. This is a hydraulically driven machine of various different sizes that has a spinning wheel on the front with teeth that grind the stump into little pieces of mulch. As it does so it mixes with the surrounding soil so you are left with a mixture of soil and very fine mulch. This is often left to settle over next couple weeks to fill the hole where the stump was and any excess spread around the garden or can be removed if required.
If the stump is in an extremely awkward position or too close to structures or important services (i.e. Gas and water) it may not be possible to grind it out without damaging any infrastructure. In this case the stump often has to remain and is subsequently cut to just above ground and poisoned to prevent any re-growth. In many cases the extra cost of grinding or the fact that the stump is not aesthetically displeasing to the client can also mean that the stump is just left and poisoned as well.