Animators have a wide variety of ways to tell the audience what kind of character they're dealing with. Red eyes indicate a character is dangerous or evil. Blue eyes can represent innocence or coldness. Sometimes, eyes glow as a show of power, or turn themselves into unusual shapes in response to different emotions.
And then there are these.
Since the 1940s, eyes drawn with concentric circles (sometimes spirals) have represented mental instability. These circles naturally draw the viewer's eye towards the center, where the irises are often significantly smaller than usual. This gives the impression that the character is staring ahead deliriously, sometimes with an intense, single-minded focus that's not found in sane individuals. If the character's eyes are the main focus of the shot, it can even look like they're gazing past the fourth wall and directly at the viewer.
Typically, a character showing Crazed Concentric Eyes won't start the work with them. Maybe they've gone through hell earlier in the story, and now they have completely snapped. Maybe they were hiding behind a Mask of Sanity, and now that The Reveal has happened, they now have free rein to show off their madness in all its glory. In either case, this trope often punctuates especially scary scenes or climactic plot developments. If someone has them by default, then all bets are off.
Compare Mind-Control Eyes and Hypnotic Eyes, which can also look like concentric circles, and Twitchy Eye, which also shows that a character is unstable. No relation to Heavenly Concentric Circles or Mad Eye, despite the name.
