I naively thought this was one of those DSLR lens cleaning bellows at first, but it's actually a gun. The Palm Pistol is an "ergonomically innovative" single-shot pistol intended for those with manual dexterity issues, such as arthritis, by using the thumb rather than the index finger to fire. That apparently reduces muzzle drift, so you're more likely to hit a target first time (which, considering there's only one bullet, is probably a good thing).
Designed by certified NRA instructor Matthew Carmel, the Palm Pistol is classified as a "standard pistol" by the ATF and can be used with a laser targeting sight. It all seems a little bizarre to me; I know it's not only the elderly who have trouble with hand mobility, but I'm imagining rest-homes full of gun-toting pensioners and some serious arguments over what TV channel is on.
Estimated price is around $300, with a $25 deposit if you want one of the initial production run. I think Core77 said it best: "Just because bystanders are screaming doesn't mean your joints should be."