The Evolved are a type of special infected in ZombiU. These infected are very rare to find, with only four of them being encountered in the entire game. Keep in mind that they are very dangerous enemies and should only be fought with good equipment. The Benelli M4 shotgun is a great weapon against these foes.
As for abilities, these infected have unique abilities. They are capable of teleportation, often doing this when damaged and can also emit a charge of electricity that will disable your prepped pad for a short while. Evolved infected have a spooky appearance, probably from degrading over time. They are distinguished by their white aurora around them.
The first Evolved is encountered in the nursery. This one was a nurse named Gillian Thompson who became infected and ate all the staff and children of the nursery. It is fought in the building's storage area. If you attempt to loot the Evolved nurse after you have killed it, it will get up and scream in your face one last time before falling back down. The second Evolved can be encountered in the underground dungeons of the Tower of London after the player returns there to retrieve one of John Dee's letters. Unlike the other Evolved, this fight is the only one that can be avoided completely by not visiting the dungeons. The third and fourth ones are found in Buckingham Palace in the room before finding Dr. Knight.
As to how they got their powers this is unknown. Perhaps they got infected by a certain strain of the virus or were just infected for a very long time.