Lucky Pokémon are a new feature available exclusively to Pokémon GO. When you trade Pokémon with other players, there's a slim chance that the Pokémon will be a Lucky Pokémon.
These Pokémon are special in that they will require significantly less Stardust to Power Up so you can get them to the max level a lot quicker than usual Pokémon. In addition to this, the Pokémon is guaranteed to have high IVs of at least 10 in each stat.
The chances of getting a Lucky Pokémon is yet to be determined, but the longer a Pokémon has been in storage before being traded, the higher the chances of being a Lucky Pokémon.