A character "gains" a permanent injury when he gets knocked down to 0 hitpoints in battle, but in the end survives. If a character can survive the battle, it will show that they are "struck down" instead of "killed" in the battle log at the top left corner of the battle screen and is also seen after the battle is over by their character panel being surrounded by a blood red border with a description of the new permanent injury. (-> an image of this would be nice, if someone could add one and then remove this note) A struck down character doesn't survive if you retreat from the battle rather than winning it.
Units with "Survivor" trait currently have a 90% chance of surviving when they are reduced to 0 hitpoints unless they are killed by a fatality or you retreat from a battle they got struck down in. It has also been reported that accumulating every single permanent injury prevents all units, even Survivors, from coming back the next time.
Units without the "Survivor" trait only have a small chance of being "struck down" rather than "killed". Note: Struck down characters cannot be eaten by nachzehrers etc. or animated by necromancers.
It is currently not possible to remove a permanent injury once received. Whether there will eventually be an extremely rare potion or event to cure one permanent injury is up for discussion and not known at this time.
Broken Elbow Joint
A broken elbow that never fully healed hinders all movement of the arm and severely reduces combat effectiveness.