During each of your opponent's end steps, that player has to choose two creatures he or she controls, then sacrifice the rest. Against aggressive strategies, this is absolutely devastating. While not every deck focuses on having lots of creatures out at one time, the Archfiend can turn up whenever an opponent is trying to win by just turning a bunch of creatures sideways.
There are quite a few decks that rely on creating lots of tokens or casting tons small creatures in order to simply overwhelm opponents. The Archfiend can absolutely punish these strategies. With Fate Reforged introducing the Manifest mechanic and Elves becoming more of a force due to cards like Collected Company and Shaman of the Pack, the Archfiend would drop in from time to time out of the sideboard to say hello.
Why didn't he see more play in Standard, though? Having a 5/4 body is cool, but that means it died to things like Stoke the Flames and Languish in the Standard of the day. In Modern, there's Path to Exile, Dismember, and Fatal Push. Still, the Archfiend only has to survive one turn with your opponent having to sacrifice a bunch of creatures to it for it to be worth casting. Best of all, the Archfiend never hurts you at all.
In Commander, the Archfiend of Depravity is a killer. Not only are Demons a popular tribe, but Black decks love things to die. The Archfiend makes even more things die, as his effect is extremely powerful in a multi-player setting. It's not surprising that the Archfiend is at home in many Commander decks.
Archfiend of Depravity may never be a main deck play outside of casual "kitchen table" Magic and Commander. But, if you're in a metagame where aggressive creature-based strategies are taking over, you may see him drop in. Decks that depend on their board states being filled by armies are sad if the Archfiend of Depravity says hello.