From Diablo Wiki
E-Peen is short for "e-penis." This is a joking term that refers to a player's desire to show off the magnitude of their game accomplishments.
Common usage would be something like, "I just found an awesome new item. My e-peen has grown!"
- See more reference terms.
One of Blizzard's April Fools' jokes in 2010 was a fake World of Warcraft system called EPEEN. "Equipment Potency Equivalence Number." This was a rating system that would have let players know exactly where they stood in regards to other WoW players. A quote from the "How Your Number is Determined" section:
Though Blizzard created this as an April Fool's joke, many fans endorsed the idea of actually having such a number, as a sort of player competency system. This would have been helpful in WoW since the end game content was all about raiding, and one player with junky equipment or who didn't know what they were doing could ruin the raid for an entire group, and there was really no way to know if a stranger could hack it until you saw how they fared under enemy fire.
The same is true of Diablo players, but since the game isn't designed to be group-dependent, and since players generally have to spend some time playing alone (unlike WoW players they can't just be carried along by the group) to achieve a high level, it's not as important if someone else can play, and it's generally a safe bet that they can, at least a little.