It refers to Section One of the Fourteenth Amendment, which says that no state may, 'deprive any person of life, liberty, or property, without due process of law.'
American President Barack Obama called the decision a, "victory for America". Adding that, "When all Americans are equal, we are all more free."
The White House's Twitter account has changed its avatar to a rainbow-coloured image of its namesake.
Jubilation came from elsewhere, too. Facebook has introduced a tool which allows users to put a rainbow filter over their profile picture, and Google have added pride-inspired artwork to searches such as 'gay marriage' or 'LBGT'.
Here in the UK, the decision is being celebrated with parades.
Although many have responded positively to the decision, there have also been those not in favour of the ruling.
Focus on the Family, a Christian organisation based in America, released a video with its President, Jim Daly, describing the decision as "disappointing".
Greg Abbott, the Governor of Texas, said that judiciaries, "have imposed on the entire country their personal views on an issue that the Constitution and the Court's previous decisions reserve to the people of the states".
Texas is one of the 14 states which will now have to change their stance on same-sex marriage. Others include Alabama, Georgia and Ohio.