The reason most death row inmates spend years on death row is due to the appeals the death row inmate has the right too.
Sometimes a person may be put on death row by mistake and it may turn out that the death row inmate is not even guilty of doing a crime they are on death row for.
So we cannot just execute the death row inmates right away even if we know the person is guilty of the crime they committed.
Sometimes an inmate may not be granted an appeal in some cases but in most cases a death row inmate will be granted a few appeals and once those appeals are exhausted then the inmate will be put to death which can happen 15 to 20 years after they are put on death row.
In some rare cases the death row inmate could be brought off death row right when they are being put to death and then they can either be found not guilty or they may have a sentence changed from death penalty to life in prison.