Pinfire is where the firing pin is part of the case rather than part of the gun, it sticks out of one side and hits a primer on the other side. It was used before the development of reliable rimfire or centrefire cartridges.
http://cartridgecollectors.org/cmo/cmo10sepc.jpg
http://freemycollection.com/content/...risPinfire.jpg
Pinfire revolvers are pretty easy to spot because they have a distinctive hammer that arches over the top of the cylinder to press down on the exposed firing pins and there are small holes in the cylinder rather than recesses with nipples for percussion caps, like so:
https://www.riverjunction.com/assets...revolver-1.jpg