An eon is a really, really, super-long, impossible-to-measure length of time. If you sit down to dinner hanging your head and moaning that it's been an eon since you ate anything, you’re exaggerating. Four hours ago is not an eon.
Eon goes back to the Greek aiōn, "age." An age is not easy to measure, and neither is an eon. Both are just really long periods of time, but in science an eon is about a billion years. You can use the noun eon for anything that takes a long while, including how long it will be before another planet collides with Earth or how many days until summer vacation starts — one is an eon, the other feels like an eon, or forever.