Quinn Worldwide is a multinational business founded by Ian Quinn. Quinn Worldwide appears to be a business encompassing many fields, with mining being one of the major activities Quinn Worldwide invests in. On one such mining operation, a large sample of gravitonium was found. That sample remains the only known quantity of gravitonium found larger than a molecular state.
In "The Asset", Quinn Worldwide kidnapped Dr. Franklin Hall from a secure S.H.I.E.L.D transport convoy to develop a way to control the element of gravitonium. Hall was the leading researcher on gravitonium, as well as the one who discovered the element's existence.
Having found the only known sample of the rare element during a mining operation, Hall was put to work to develop a way of containing gravitonium safely and harnessing its power for Ian Quinn's use. Realizing that gravitonium was too dangerous for any person to use, including Quinn Worldwide and S.H.I.E.L.D, Hall shocked the element into an overheated state, causing it to suck up anything in the room, including all of the Hall's research and Hall himself.
In "Seeds", Ian Quinn was approached by S.H.I.E.L.D student Seth Dormer, who had convinced fellow student Donald Gill to build from the research of Jemma Simmons and Leo Fitz to make a weapon, intending to sell it to Quinn Worldwide. Intrigued, Quinn Worldwide allowed them to work on the weapon and later prove that it worked.
After multiple incidents with students suddenly freezing into ice, Dormer and Gill were discovered and ran off, going to an empty lot and activating the device outside for Quinn to see. The device became out of control, creating a massive and deadly hurricane-like storm, where Dormer was killed. After the device was shut down, Quinn Worldwide worked to walk away from the "incident".
In Season 2 neither the company nor its CEO has been seen or heard of, although the gravitonium is around.