Volibear is a very powerful and robust tank, with offensive capabilities scaling off his ability to endure punishment. His passive may be the one reason his role as a tank shines despite his lack of defensive abilities, healing him for 30% of his max hp. Aside from that, Volibear is also very dangerous in that his Frenzy can potentially prematurely shut down an enemy carry, but the long cooldown on his Frenzy skill makes it have limited use.

As a tank, you must be ready to charge in and take hits for allies even if it means dying in the process. This doesn't mean you should die every chance you get for the sake of pride. This means if you and your carries were getting chased, prioritize their survival over yours. This will lower the amount of time they spend -dead- and more time farming/killing. The stronger they are, the better damage output the team as a whole can produce.

Keep in mind, it's always better to save people from dying WHILE staying alive as well compared to dying on every heroic attempt. No one likes a feeder, no matter how you died.

Note: The table above showing champion final stats don't entirely match up with reality. It doesn't add developed bonuses such as the potentially gained 350 hp per Warmog's Armor or hp bonuses from Mastery/Runes. Here these calculations have applied all bonuses and are the true final stats of Volibear depending on the build discussed.

Tank Build 1

Hp = 1.12(1988+1270+375+108+30)= 4223(2235 as bonus)
Atma's Damage Bonus= 84
Frenzy's Initial Damage= 260+(15% health bonus)= 260+335
1% of health bonus= 22
Frenzy Damage on Enemy at 65% HP= 1377
Frenzy Damage on Enemy at 50% HP= 1712
Frenzy Damage on Enemy at 35% HP= 2048

Tank Build 2

Hp = 1.12(1988+3(1270)+108+30)= 6648(4660 as bonus)
Atma's Damage Bonus= 132
Frenzy's Initial Damage= 260+(15% health bonus)= 260+997
1% of health bonus= 46
Frenzy Damage on Enemy at 65% HP= 2690
Frenzy Damage on Enemy at 50% HP= 3289
Frenzy Damage on Enemy at 35% HP= 3988

Tank Build 1

Total cost: ~14,000g

Relatively cheap build, provides over 200 armor and magic resist while providing a meaty 4k+ hp pool. Thornmail helps chop those nasty AD carries down, allowing for Frenzy to 1 shot anyone if their health is at a low enough %. Banishie's Veil is important for periodically blocking one of those key CC skills that lock you down before you can disrupt team formations and positioning of enemy carries. Exclusively usefulness of Merc Treads are largely self explanatory for their function, allowing one to ignore a certain stuns/snares/silence/slow like Veigar's stun or slowing rapid CC dealers like Amumu and Leona.

Tank Build 2

Total cost: 15,100g

Providing a massive 6.5k hp pool while sporting 124 armor and 153 magic resist, this allows for enduring heavy punishment while giving you lots of time to do plenty of damage (better with your ult active). Frenzy should be strong enough for someone to take out or nearly kill any carry if provided some extra damage from anyone like Xerath's Q or R.

Greater Mark of Desolation
Armor Penetration
Very effective in making your Frenzy deal it's full damage.

Greater Seal of Endurance
Health Percent
Helps get you that extra couple hundred hp and is useful from early to late game.

Greater Glyph of Clarity / Greater Glyph of Shielding
Cooldown Reduction / Magic Resist
CDr helps allow for more frequent skill activations, also allows for an edge in better crowd control.

Greater Quintessence of Endurance
Health Percent
Adds lots of extra hp, why not?

Heal

This is mainly chosen to allow for Volibear's passive to successfully heal him when the danger arrives. Most of the time when the passive would trigger, the enemy champions should have already planned for enough burst damage to kill him before his passive can trigger and complete it's healing. Since his passive only triggers when hp drops below 30%, this puts him in danger of burst damage champions. To counter this, Heal can offset their chances of landing a kill and possibly become a baiting tool for unsuspecting ganks.

Cleanse

This champion shines best when the passive surprises enemy teams and deprives them of a kill and forces them to waste more efforts focusing on you the tank instead of friendly carries. As a tank, the worst that could happen is getting locked down by something like Exhaust and becoming unable to interrupt enemy formations. Having this can resolve this issue without having to waste an item slot on a Black Belt.

Flash

When you feel brave in attempting a non-ranked game, Flash can be an excellent add to Volibear. Since all his abilities require him to be close up and predictably avoidable, Flash will allow him to surprise enemy champions and close up on their position. And obviously, Flash is very useful for getting out of a tough situation in case Volibear walks into an ambush/gank.