Although astronomers and geologists use the word "eon" to mean 1 billion years, it is more commonly used to refer to any long, indefinite period of time. Like the words "age," "epoch" and "era," it does not refer to a set number of years.
In ancient Greece, the word "aion" meant an infinitely long time or an eternity. Plato used the word to denote the eternal ideas that lay behind the perceived world. Geologists divide the history of the Earth into four geologic eons. The latest, called the Phanerozoic Eon, began 540 million years ago and continues into the present day.