The literary term for exaggeration is hyperbole. Hyperbole is a figure of speech used by a writer to overemphasize a point. It is not meant to be taken literally but is intended to give the reader a "larger than life" picture to highlight a particular idea.
Writers use hyperbole in both poetry and prose, and speakers use it in everyday conversation. "My friend always shops till she drops," "He waited forever for her to finish" and "She loved the baby so much she wanted to eat him up" are all examples of hyperbole one hears in normal conversation. None of those statements is the literal truth. People normally do not shop until they fall down on the ground, no one literally waits forever for someone else to finish something and love does not actually make someone want to eat another person. These are just exaggerations to emphasize a point. A good example of hyperbole is found in a Paul Bunyan tale: "“Well now, one winter it was so cold that all the geese flew backward and all the fish moved south and even the snow turned blue." None of those things happened, but the writer surely painted a strong picture of how cold it was. Hyperbole is the opposite of understatement.