A pin feather is a developing feather. A bird has down feathers when it hatches, and it grows mature feathers a few weeks later. Birds also grow new feathers after they have lost feathers during a molt. A pin feather looks like a small feather shaft.
Because a pin feather is still growing, it has a supply of blood flowing through it. If a pin feather is damaged, it will start to bleed. To stop the bleeding from a damaged pin feather, simply remove the entire feather from the skin follicle.
For more information, refer to the article "Anatomy of a Feather."