"Boneless" was the name the Twelfth Doctor gave to creatures from a two-dimensional universe. They were able to reduce both lifeforms and other three-dimensional objects to two-dimensional. After taking on three-dimensional forms themselves, they were also able to restore objects back from two-dimensional to three-dimensional. They also demonstrated the ability to drain dimensional energy from the Doctor's TARDIS, causing its external shell to be drastically reduced in size and weakened.
History
The Boneless experimented on and dissected three-dimensional lifeforms and objects, and eventually learned how to exist as three-dimensional beings themselves. Their transformation into 3-D beings was not perfected however, resulting in an appearance where they seemed partially 3-D and partially 2-D.
The Doctor had hoped that their experimenting on the humans in Bristol was strictly due to some misunderstanding; the Boneless originated from a universe with only 2 dimensions, and therefore were unable to communicate in a language that 3-D organisms could comprehend. However, following some experimentation he was able to establish rudimentary communication with them, consisting only of sonically encoded numbers. Their subsequent naming of the numbers on the jackets of both a previous victim and their next victim convinced the Doctor they were likely able to read, and were thus aware of what they were doing.
Satisfied that he had given them a fair chance, and that they could indeed understand him, the Doctor used his sonic screwdriver and an energy field from the TARDIS to forcibly send them back to their home dimension. He did so without regard to their chances of survival on the return trip, and with the following warning to any more Boneless who wished to conquer the 3-D universe: "You are not welcome here! This plane is protected! I am the Doctor!". The Doctor didn't know whether the Boneless entered the 3-D universe to invade, infiltrate or just to "replace" humanity, but he believed that the role they "seem[ed] determined to play" was that of "monsters", with him being "the man that stops the monsters." (TV: Flatline)
References
As one of the aliens she had met during her travels with the Doctor, the Boneless were included in a series of notes written by Clara when she was planning to confess to Danny Pink via phone call about her continued adventures with the Doctor after previously telling him that she has ceased travelling with him. (TV: Dark Water)
After the Twelfth Doctor's mind was connected to a mind scythe, the "holiday snaps" the Doctor showed Kygon Brox included the Boneless. (COMIC: The Instruments of War)