The case brought up the issue of the Constitutionality of the Death Penalty and whether such a penalty violated the 8th and 14th Amendments.
The 8th Amendment forbids "cruel and unusual" punishment; the Supreme Court ruled that although such an injunction exists, the amendment does not forbid humane execution. The Court further ruled that other amendments to the Constitution implicitly acknowledged the death penalty; the 5th Amendment states that "No person shall be held to answer for a capital, or otherwise infamous crime..." and the 14th implies the penalty by stating that "no State shall deprive any person of life, liberty, or property without due process of law."
The Court determined that although not stated, the Framer's intent in the 5th and 8th Amendments was to allow for a Death Penalty.
Although the Court admitted it to be the most extreme of punishments, it concluded that the State of Georgia, in sentencing Gregg, did not violate the Constitution.
Interestingly, the Court also noted that although juries over time had become more reluctant to impose the Penalty due to its irrevocability, it was in place for use in precisely those few rare cases where justice demanded it.