Poor J.J. He was always kind of the Ringo of the group—beloved, but ultimately forgettable. He didn't even have a memorable name—John Jay kind of sounds like something you'd make up to win an argument: "Yeah? They told you that? Who told you that?" "My friend, um, John…Jay?"
Jay's the obscure Founding Father…even though he seems to be the one Founding Father all the other ones agreed on. Adams and Hamilton both thought highly of him, and George Washington gave Jay first pick of any cabinet position he wanted. (Jay chose the Supreme Court because he's no dummy.) (Source)
Jay was initially a moderate who, while representing New York in the Continental Congress, wanted to preserve the colonies' connections to England. During the Revolution, though, he basically radicalized and decided that Independence was the way to go.
Get it, Jay.
He served as the Minister to Spain—a diplomatic role similar to the one Franklin played in France—but was far less successful. Don't worry; being less successful than Franklin at diplomacy is a little like not being as good a runner as Usain Bolt. As the war ended, he joined Franklin in the negotiation of the Treaty of Paris.
Jay was quickly annoyed with the Articles of Confederation, and Hamilton reached out to him to start something better. Along with James Madison, the three of them got to work on the Federalist Papers, which was basically a dry run for the Constitution we know, love, and is still working after a couple o' centuries. (Source)
Jay served on the Supreme Court for six years, from 1789 to 1795. He was then elected to be Governor of New York. People loved the guy. Jay himself was a slave-owner (yes, slavery existed in the North), but was responsible for signing the law that eventually phased out the practice in New York.
Jay was a quiet guy, dying peacefully in his library at the ripe old age of eighty-three. Though he's not the most famous of the Founders, the country we know wouldn't have been possible without him.