The nature of eternity is "never dying". For humans it is the ability to have life without dependency on matter. In our current state as physical beings we need water, air and food to have what is known as life. but God says we are more than just physical. In scripture it is said that the when the body dies it is returned to the ground but the spirit is returned unto the Lord. It is also written in Hebrews that all men die once and then there is a second death. Scripture clealy state we are eternal beings meaning life after death...or as can be said life after this life.
Time is created by God for man to date himself in this world system. Adam, the first man we can be assure of had no concept of time because God had not decree a system of tracking at that time. For instance the earth was turning but men thought the earth was flat. Ancient men thought the sun went up and down but now we know the earth turns!! In fact, I speculate that a dating system did not truly exist on a world scale until Jesus came and a few hundred years later we get the BC/ AD decree.
This is interesting, because you have to ask the question how did the world date itself before Christ. In general it didn't on a world scale. Nations did there own thing with time and it didn't work for other nations who had their own system. The Jesus reference dating allowed all to track things before him and after him. I feel Time is only applicable for earth and can't be applied anywhere else in the universe. If the earth did not rotate would time be measured differently? Not all planets rotate. That's my 2 cents.
Your question is a good one. The bible promises man an eternal existence and Christ came to prove life after death and said one day he will return. Perhaps to prove eternity does in fact exist and is a goal worth seeking for in our short life span on this planet.