Cause: I'm not sure. Obviously he injured it somehow, but I don't know how. Maybe he got it stuck somewhere and yanked it loose? Or if he was trying to get through a fence, he might have banged it way too hard?
Treatment: time, and food that is soft and easy to eat.
I suggest putting some chicken food in a dish, and adding water so it gets all soft.
Make sure it's deep enough that he will not stub his beak on the bottom of the dish.
If other chickens pick on him, he may need to live separately while it heals.
Or he may need separate mealtimes, so he can eat carefully without hurting his sore beak.
Or he may be just fine living like normal, as long as you put out a nice dish of food regularly. (Wet chicken food will not hurt other chickens, if they eat it too. Just make sure the rooster has enough when he needs it!)
The hard part of a beak grows from the base out toward the tip (rather like toenails do). Over the course of a few months, he will probably grow an entire new outside for his beak, and the damage will slowly work its way down toward the tip until it is all gone. The end usually gets worn down by the normal chicken actions, but if the beak is sore he may not do that. So it it gets really long, you may need to carefully clip a little bit off the end every now and then. Only clip the very end, so you don't hit the part with nerves and blood inside, and do not clip it at all until it has some time to heal and get long. You may not have to clip it at all, if the rooster wears it down normally as it heals.