Plot armor is a term used in fandom to describe when a character or characters are invincible by authorial fiat despite any rules or logic established in the setting. In story telling characters face and overcome threats. The scale and nature of those threats establish the stakes of a given story and through strength, skill, savvy, or virtue the protagonist overcomes and we get the catharsis of the story. One of the ways to win not listed is luck. There is nothing intrinsically wrong with a lucky break for the main character. What isn't okay is when the protagonist wins because of one lucky break after another, the cavalry arriving just in time, a new highly applicable super power, or the villain losing despite having displayed significant competence previously.
Challenge and conflict or the lifeblood of fiction that makes it worth reading and every story carries an implicit agreement between the author and his audience that the world of the story will abide by certain rules of internal consistency that calibrate expectations. The bigger the challenge the greater the excitement and catharsis so it behooves writers of exciting fiction to really crank up the tension to the maximum. Plot armor is what happens when authors' capacity for writing challenges exceeds their ability to write resolutions. A character with plot armor is never in real danger because they will never to get into a situation that they won't get out of. If the audience knows that a character won't face consequences then the highest stakes in the multiverse don't mean jack.
The term plot armor, like mary sue and deus ex machina, gets thrown around when a fandom have something to kvetch about and are highly subjective. Fictions that are deliberately more style than substance get a lot of leeway in making sense while stories that are anal retentive about explaining their magic systems better stick to the rules they lay down or come up with very convincing reasons why they broke them. While pervasive plot armor is likely to be the death of a work; it's often limited to one or two characters that the author has some attachment to and remain a minor irritant on the fandom.
IRON NODER THE THIRTEENTH