The word “hyperbole” (an obvious or extreme exaggeration) is via Latin, from the Greek hyperbole, which was used to mean “exaggeration, extravagance” but literally meant “a throwing beyond.”
The Greek hyperbole is formed of hyper- “beyond” + bole “a throwing, a casting, the stroke of a missile, bolt, beam.” Bole is the nominative stem of ballein, “to throw,” from the PIE root gwele- “to throw, reach,” which also influences words such as ballistic, ballet, metabolism, parable and symbol.
There was also a Greek verb form, hyperballein, which meant “to throw over or beyond.”
The English pronunciation of hyperbole (high-PER-boh-lee) comes from the Greek pronunciation (ὑπερβολή). The Greek letter eta (ή) does not correspond directly to any English vowels, so it’s usually written as an E, which results in borrowed Greek words that diverge from typical English pronunciations. Think of the pronunciation of name endings like Hercules (Ηρακλής).