Eternity means "forever," like living for all eternity. Or it can mean something that seems like it will go on for forever, like waiting an eternity for your sister to get out of the bathroom.
Eternity means "time without end, or infinity," like people who promise to love one another for eternity — they aren't planning to ever split up. When you put the word an before eternity, you can use it to describe a very long — too long — period of time, so that you can use it to complain. For example, you might use the phrase "it felt like an eternity," after waiting twenty minutes to get an ice cream cone.