A Nest Pass is an item required to enter a Nest and one is consumed upon entry. As of October 24, 2012; only Archbishop and Titan nests require a nest pass.
Normal Passes are used to access the Abyss version of each Nest and are obtained from a Dimensional Rabbit's box. Rare Passes are needed to enter the Hell versions and can only be obtained from the Reward Chest in the Abyss versions of the corresponding dungeons.