A stump is the bit that gets left when a tree comes down, and it tends to stay there for years. You mow around it, you trip over it, and it sits exactly where the patio or the shed needs to go.
Grinding takes it out below ground level without digging up half the garden. Once it is done you can lay turf, pave or plant over the spot, and it stops throwing up new shoots.
It does not matter who took the tree down. If you had it felled by someone else, or the stump came with the house, we can still come and deal with it.