Forceps in fly fishing are used to remove the fly from the fish. You'll need them when the fly is difficult to remove because it's deep in the fish's mouth or because it's just hard to get out (you might be using a barbed hook).
Some forceps have a little spike in the middle. You can use this if the eye of the hook on your fly is obstructed, mostly caused by excess glue from fly tying, by pushing the spike through the eye of the hook.
Want to read more about fly fishing accessories? Check out our list of the essential fly fishing accessories.