This video shows you a fun and popular demonstration of the power of sulfur hexafluoride. The gas makes a tinfoil boat float, seemingly on nothing. It's a reminder that the substance we think of as "thin air" can exert pressure. Which is why this gas might get injected into your eyeball.
Sulfur hexafluoride is a combination one sulfur atom and six fluorine atoms, and to synthesize it all a chemist has to do is expose sulfur to fluorine. You don't want to make too much, though, because it's a greenhouse gas. You also don't want to let it loose in the environment. Although it's dense enough to sink to the floor, it displaces air and too much of it can suffocate a person.
People who do run into trouble with it generally do so when they're demonstrating sulfur hexafluoride's affect on the voice. When inhaled, helium makes a person's voice high and squeaky, but Sulfur hexafluoride makes a person's voice deep and booming. The difference is it's harder to get sulfur hexafluoride out of the lungs because of its relative density. It doesn't do any damage per se, but it can deprive people of oxygen.
The combination of staying power and lack of damage is what caught the, ahem, eye of the medical community. As a substitute for oxygen, sulfur hexafluoride is a disaster. In and of itself, it's harmless. That's a good combination.
Ocular surgery is complicated by many factors. It deals with delicate tissue, which is always moving, and which doesn't do well with repeated interventions like stitch removal. Sulfur hexafluoride proved a perfect way to deal with torn or detached tissues inside an eye. In the case of an injured retina, for example, doctors could inject sulfur hexafluoride. It would put pressure on, and consequently flatten down, retinal tissue. The gas was as gentle on the tissue as anything could possibly be, allowed the eye to move, and slowly disappeared over the course of two months, without any interventions. (In contrast, air dispersed over two weeks.) Physics and medicine came together and gave doctors a perfect material — that we all hope never gets used on us.