Barbless hook
A barbless hook is a hook without a barb. Fly fishing with a barbless hook means that you really have to keep the line tight while fighting the fish, because if you loose the tension on the line the hook can more easily slip out.
That's also the advantage of a barbless hook: it's easier to remove it and thus does less damage to the fish.
If you have a barbed hook you can remove the barb by squeezing it flat with pliers or your forceps.
A barbed and a barbless hook