Hyperbole
Etymology
From Greek hyperbolḗ, "excess, a throwing beyond," from hypér ("over, beyond") + bállein ("to throw"). The image is of a throw that sails past its mark. The same word gives geometry the "hyperbola," but in rhetoric it settled on overstatement so large it announces itself as figurative.
noun · /hy-PUR-buh-lee/
Deliberate, obvious exaggeration used for emphasis rather than to be believed literally.
What it names
The engine of "I have told you a million times" — overshooting the truth so far that everyone reads it as feeling, not fact.
Example
His hyperbole was doing all the work: "This is the greatest sandwich in the history of civilization."
Related idea
Understatement is the mirror image, shrinking rather than inflating; both distort scale on purpose, but hyperbole overshoots and understatement undershoots.