The flat part on the left is for cutting clinches. Here's another photo. 
This picture shows how the clinches are cut. When a horse shoe is nailed on, the nail has to come out of the hoof wall. The nail is then cut off, and clinched over to hold the shoe tight on the foot. The horses foot will grow about 3/8's inch a month, and the army required the horses to be shod every 6 weeks. Because of the cost of shoeing today, most people leave the shoe on as long as possible. But when it's necessary to remove the shoe, those bent over clinched nails have to either be straightened out or cut off, and then large nippers, which are called pull offs, are used to remove the shoe. The other end, or spike looking thingy is used to pull an individual nail. 
Note the crease in the shoe where the nail holes are. The heads of the nails fit down in that crease so that as the shoe wears the nail heads don't wear off, but wear down with the shoe. Now lets say the the horseshoer screws up and quicks the horse, which means he drives the nail into the tender part of the foot, like getting a sliver under your finger nail. That nail has to be pulled out, but nothing can grip the nail head to pull it, so the pointy thing on the clinch cutter is driven into the crease and under the nail head, then pried up, and by working back and forth on both sides of the nail it's pulled out enough that nippers can finish the job of removing it. That's over simplified, so I hope it's understandable. Of course the tool could be hand made by the shoer himself, lots of guys make a lot of their own tools. Also the clinch cutter pictured is a modern version, I found an old one that is totally different than this one. I shod horses for enough years that my clinch cutter was pounded down below the level of the handle, not even with the handle like the one you have.
