Volibear's W scales to health. It's also an execute, so it scales to his target's missing health. Also, his W's passive gives him attack speed. And that actually makes his R somewhat useful.
If you see a Volibear build an Atma's Impaler, now you know you're really in trouble.
But with health and armor, it's extraordinarily difficult to do much damage too him. One thing you can do (for now, until it gets removed) is get someone on your team to build a Madred's Bloodrazor. Also, Deathfire Grasp is useful if used at the beginning of the fight. There may be other items too, but basically you're looking for items and abilities that do percentage health based damage.
EDIT: Also, Volibear's passive. When he gets below 30% health, it heals him for 30% of his health. So a Volibear with 6,000 health essentially has more like 7,800 health that you have to chew through. And that's even more effective health when you count in armor. So another strong play against Volibear is Ignite (or any item or ability that causes reduced healing effects). Putting ignite on Volibear before his passive kicks in cuts his passives heal in half.