So, if a Knight Radiant were walking along and cut himself, then breathed in stormlight, the stormlight would immediately recognize that the cut does not fit with the knight's perception of himself and begin to heal the cut.
So here's my example:
A knight radiant is charging along in battle with his comrades when they are attacked from behind. The group breaks rank and swivels about to face the ambush, but the knight radiant aforementioned is too slow and is thrown to the ground by one of the enemy monsters. One arm is pinned under the creatures foot and the other hand is caught under a rock. Unable to summon his shardblade and unable to use surgebinding because he is a Edgedancer and not even resurrecting a dead boy will save him, the knight watches helplessly as the monster lifts its massive club to mash in his forehead.
Except... he doesn't watch helplessly! He has a hidden power! He immediately convinces himself that he has a third arm sprouting out of his chest, only he lost this arm during the battle. It was very painful. The stormlight immediately sympathizes and helps him by healing his third arm which miraculously appears out of his chest, summons a shardblade, and slays the monster.
He then is made fun of by his peers because he is deformed and amputation doesn't help at all.