From Bulbapedia, the community-driven Pokémon encyclopedia.
Egg cycles are a number that determines how long it will take for a Pokémon Egg to hatch. The value of the amount of Egg cycles remaining until the Egg hatches is stored in the same number that the friendship value is for normal Pokémon, however, rather than counting up after 255 steps have been taken, it counts down toward hatching on reaching 0.
Whenever the player receives or hatches an Egg, the current Egg cycle of all other Eggs in the player's party are decreased by one.
Individual Pokémon species have a value for the amount of cycles an Egg of theirs will take to hatch when received by default, however, the cycle's value, if altered, can be as high as 255 for an individual Egg.
Please note that not all of these species can be legitimately hatched from an Egg, and that all steps are the minimum numbers as of Generation V.
List of Pokémon by base Egg cycles