A DPS meter is a program or system found in many RPGs that measures a character's actual damage output over time. Rather than the approximate/estimated value that the damage number shows in the character window in Diablo 3 (and the previous games in the series) a DPS meter records or estimates actual damage output.
Many fans would like a DPS meter in Diablo 3 since the number in the character window, the so-called Sheet DPS can be very far from accurate since it does not include important factors such as Elemental Damage, damage bonuses against Elites or Demons, and damage from bonuses to individual skills, Many players have an Effective DPS 2 or 3x higher than their Paper DPS displays, and thus wish for a DPS meter to get an accurate reading.
Blizzard has acknowledged that the DPS display in game is inaccurate and merely an approximation, but they have also repeatedly stated their lack of interest in fixing it, or implementing a DPS meter. And since they also disallow player modding or UI improvements, players will continue to ask while using third party sites to see more accurate analyses of character stats.