If someone is hyperbolic, they tend to exaggerate things as being way bigger deals than they really are. Hyperbolic statements are tiny dogs with big barks: don’t take them too seriously.
Hyperbolic is an adjective that comes from the word hyperbole, which means an exaggerated claim. The Greek root huperbolē means “excess,” and broken down even further the word literally translates as “throw above.” Imagine tossing a football to a friend, but you throw it way above their head and onto a roof. That’s an excess of throwing, and it’s not necessary, which is exactly what being hyperbolic is all about: making statements bigger than necessary.