Eon has a number of meanings. In Astronomy an eon refers to 1 billion (##10^9##) years. But it also refers to a very long unspecified period of time or specific geologic stages of .
Since this question is posted in Astronomy I will assume that the answer of eon = ##10^9## years is the most appropriate however it is not the most common.
The term eon (or aeon) is frequently used as a term for a very long but un-specified time period much the same way forever and ages are used.
In Earth history stages of the earth’s development are divided into four major eons (Hadean Archean Proterozoic and Phanerozoic) which are in turn divided into eras and periods. These geologic eons are distinguished by major stages in Earth’s geologic history rather than fixed periods of time.