What is the significance or impact Gregg vs. Georgia has on American society?
In Gregg v Georgia (1976) the US Supreme Court overturned its previous decision in Furman v Arizona (1972) that the death penalty was unconstitutional. The Court's ruling in Furman was concerned largely with the form in which the death penalty in the United States is carried out rather than the substantive issue of whether it is an appropriate method of punishment. Specifically, the Court's decision related to procedural safeguards (or lack of them) in response to growing concerns about the impact of the death penalty on socially-marginalized groups.
The formal nature of the Furman decision essentially gave a green light to those states with the death penalty to tighten procedural safeguards against possible injustice rather than abolish the system altogether. The wider question of whether the death penalty is morally justified or whether it's an effective crime prevention measure was ignored.
It was somewhat inevitable, then, that a future decision would re-affirm the constitutionality of the death penalty so long as the appropriate safeguards were in place. This is what happened in Gregg v Georgia. The question before the Court was not whether the death penalty constituted "cruel and unusual punishment" under the Eighth Amendment, but whether it had been properly administered.
The greatest impact of Gregg v Georgia has been a significant increase in the number of executions. The United States now has the fifth highest execution rate in the world. The proportion of non-whites to whites on death row is now 54%, higher than the 50% it was before Furman. It's rather ironic that the Supreme Court initially struck down the death penalty on the grounds that it was unfairly administered, and yet now the evidence seems to suggest that it's more unfair than ever before. Arguably, this is a direct consequence of the Court's dealing with the issue of capital punishment in a narrowly procedural way instead of examining whether or not it constitutes "cruel and unusual punishment" per se according to the Eighth Amendment.
The main impact of Gregg v. The State of Georgia was in the U.S. Supreme Court's decision that capital punishment (i.e., the death penalty) was constitutional so long as the procedures involved in its execution did not violate the Eighth Amendment to the Constitution. In other words, states were free to impose the death penalty, but the methods used in carrying out that penalty could not constitute "cruel and unusual punishment." A major result of that ruling by the Court was the development by the states of the practice of lethal injection. While older forms of capital punishment -- mainly firing squad and hanging -- were deemed "cruel and unusual," other, more modern forms (and, it should be noted, that death by firing squad was practiced in the State of Utah as late as the 1977 execution of convicted murderer Gary Gilmore) were still in use, including the gas chamber and the use of electrocution (the "electric chair," still in use and still controversial for the failures at times of those vested with responsibility for carrying out the execution to actually kill rather than torture through burning condemned convicts strapped to faulty electric chairs).
Gregg v. The State of Georgia, by sanctioning capital punishment, allowed individual states to continue to execute prisoners convicted of particularly heinous crimes.
The significance of Gregg v. Georgia is that it made the death penalty legal once again. The death penalty had been illegal for a few years, but it was reinstated by Gregg. The death penalty has come to be something of a hot topic in American politics. There has been a great deal of controversy over whether it should be abolished and what sorts of reforms should be made to its administration. These would not have existed had the Court kept the death penalty illegal in Gregg.
However, it seems likely that the issue of the death penalty would have become a major political issue even if Gregg had been decided differently. America is too conservative of a country (and was even more so at that time) with regard to crime and punishment to have simply allowed the death penalty to be banned permanently.