Trees, like humans, are susceptible to infection and disease when wounded, especially when the cause of the wound is poisonous. It can then be necessary to remove a tree for visual or safety reasons. In these cases, gardeners sometimes use copper nails. Since the nails kill the entire tree, there is no stump to clean up.
In cases of killing a tree through injury, the copper in the nail doesn't cause harm so much as the wound the nail inflicts. Very long, large copper nails driven into a tree trunk can pierce the cambium or soft inner bark of the tree. The cambium is like the sub-dermis in a human. If that inner skin opens, infection and disease can get in and cause sickness. Additionally, hammering nails into a tree causes stress to the tree as it tries to repair the injury. Stress makes trees more likely to attract infections and insects.
According to Penn State Extension, shiny and untarnished copper won't kill a tree. Oxidised copper, however, is covered in a tarnished coating that the tree can absorb and metabolise. As the poison builds in the tree's system, the tree dies. You can kill a tree this way by hammering tarnished copper nails into the trunk, but the job gets done faster if you bury some of the nails in the soil around the tree or hammer them into visible roots. Since roots carry nutrition to a tree, they'll pull in the oxidation faster.
Oxidising Copper Nails
Oxidised copper is basically discoloured or tarnished copper. Creating your own oxidised copper nails is no harder than leaving them out in the elements for a few weeks. Rain works especially well since the minerals in the water tarnish copper very quickly. You can also heat the nails in your oven until they turn black. As they cool, the black coating will drop off and reveal copper tarnish.
A stump can live and shoot up sprouts even after the tree has been cut down. Since the roots are still intact, the stump is still technically alive. Instead of trying to yank it out of the ground by the roots, weaken it a bit with some copper nails. Hammer a few nails into the roots and top of the stump. It may take a few months, but the stump will eventually die and begin to crumble. You can then dig up or pull out the stump with much less hassle.