This is the the Palm Pistol, from Constitution Arms in New Jersey, an interesting take on a very concealable, last ditch weapon. It is a single shot, breech-loading pistol.It is chambered in the popular and soft-shooting .38 Special cartridge which is widely available and cheap. (well, used to be) Other than its extremely unconventional layout, the main design difference between the Palm Pistol and just about every other gun is that you fire the weapon with your thumb rather than your index finger. The idea is that doing so will reduce muzzle drift, which is one of the main causes of missed shots. Also the lack of a recoiling slide and due to its extremely low bore axis, most of the recoil will be directed straight back along the line of the firer's arm, which may make it easy and comfortable to shoot.
There was some notice of it in the mainstream media (where I saw it) because the inventor claimed that this weapon would be much more suitable for people with physical disabilities and as such, should be paid for by disability and insurance. Needless to say, I don't think any
companies will be buying pistols for seniors and the disabled. The pistol will be marketed with an eye towards people with dexterity limitations or other difficulties that prevent them from operating a traditional pistol effectively. Some of the literature about the weapon also hints at its use as a backup gun and as a covert weapon, but for now I have some doubts.
If it were me, I would add a little muzzle brake/flash hider to decrease the possibility of shooting my own fingers off, or even just burning them on a hot barrel. I suppose it isn't really meant to be shot that much though.
Of course, this is not the first time a pistol shaped like this has been manufactured.