The Legendary Pity Timer is a behind the scenes game feature that ensures a player will not go much more than two hours of gameplay without finding a legendary item. It is meant as a fail safe, and most players will only very, very rarely encounter it. This is because legendary items drop quite frequently, and only an extremely rare run of bad luck will make a player go so long without finding one that the timer comes to the rescue.
There is no "official" name for the pity timer; players just call it that since it's descriptive and sarcastic.
Pity Timer Revealed
Blizzard tweaked the legendary drop rate repeatedly during Reaper of Souls testing, most impactfully in the "doubled it" buff made permanent after the week-long second anniversary buff event in May 2014. The game (in D3v2 and RoS) also has a Pity Timer that ensures a player never goes more than about two hours without finding a legendary item. Travis Day spoke about it in January 2014:[1]
The fact that some people claim to go for 10+ hours without finding a legendary is not only not our intent, but should in fact be impossible. We added a system in the expansion that tracks the amount of time you spend fighting creatures without finding a legendary and after a certain period of time will slowly start increasing the legendary drop rate. Once a legendary drops for you, actual item not crafting recipe or material, we reset that timer. This is meant to be a safety net so that the random can never be too extreme to the negative end. If players are legitimately going 18+ hours and not seeing a legendary it’s possible that there are some bugs floating around that need to be identified.
And before anyone responds saying TWO HOURS IS TOO LONG! let me say that we know as time goes on and we patch content or players get better gear and find better specs that will not be the reality. Higher difficulties do in fact increase your chance to find legendary items, coupled with people playing in coop also increasing the rate that everyone overall finds items, etc. Our final target is roughly in the 90 minute range for advanced players. This doesn’t factor in crafting items, trading with friends in coop or any of the other means that we already know players can use to accelerate their legendary acquisition rate.
Travis returned the next day to offer clarifications, chiefly about the pity timer. In them he confirmed that it was not exploitable by standing in town to let it build up. The timer only runs when players are triggering "could have dropped a legendary" events, such as killing monsters and opening chests.
First the clarification, the timer system that works behind the scenes is meant to be exactly that, behind the scenes. No you can’t AFK the system, there are a lot of moving pieces to it and we talked about it extensively before we implemented it to guarantee its not exploitable. At it’s heart Diablo is a game about slaughtering demons and getting random cool rewards. The system that is in place should never be experienced by 99% of the population, it’s there for the 1% who just get really bad random rolls for an excessively long period of time. If we want you to get a legendary every 2 hours, the system basically says “ok it’s been like double/triple that period of time, just help the guy out!”