Hyperbole is a writer's tool that features extreme exaggeration to make a point. For example, if you said "Her brain is the size of a pea," you would be exaggerating her lack of brain power. "He is older than the hills" is another hyperbole poking fun at how old someone is. The exaggeration is often used to garner a humorous response, and the advertising industry uses this technique frequently.
An idiom is a phrase that has a literal meaning and a figurative meaning but is understood at the figurative level. Many non-native speakers have trouble understanding idioms because they first analyze the literal level. "It's raining cats and dogs," for instance, means it is raining extensively, but not that dogs and felines are falling from the sky. The idiom "He kicked the bucket" means that someone has died, but a non-native speaker would picture a man literally kicking a bucket down a road.
Examples of Hyperbole
To spot the differences between hyperbole and idiom, it is important to fully understand exaggerations. Hyperbole is found in tall tales, like the stories of Paul Bunyan and Johnny Appleseed. Could one man really plant all of the apple trees in an American region? They are also used to clarify a description, because people have such different frames of reference. For instance, if you said someone had a really big house, that would be very different if the person was rich or poor. But saying “Mary’s house is so big that the entire population of the city can fit into it” really clarifies the situation. Including the specific exaggeration makes the meaning clear. Hyperbole in advertising has often earned it a negative connotation. The slogan "The best part of waking up is Folger's in your cup" is a definite exaggeration.
Examples of Idioms
The difficulty with idioms is that they are figurative language in their own right, but they have gained a meaning beyond themselves in colloquial language. For example, saying a new job is "icing on the cake" is really a metaphor, a comparison of two unlike things. American speakers have come to understand this phrase on two levels. Literally, this means that someone is putting a sweet icing on top of a cake with a spatula; figuratively this means that something great was added to someone's already-fine life. What can be confusing is that an idiom could start off as hyperbole. If someone says "That new car cost an arm and a leg," that is exaggeration to make a point. But colloquially, this has further meaning as an idiom. The figurative meaning is that it is so expensive that you would have to give up a lot to have it.