It can also mean existing altogether outside of time. Augustine of Hippo wrote that time is a part of the created universe, so that God exists outside of time; for God there is no past or future, but only an eternal present. That position is accepted by many Catholic theologians. One need not believe in God in order to hold this concept of eternity: an atheist mathematician can maintain the philosophical tenet that numbers and the relationships among them exist outside of time, and so are in that sense eternal.
Theists say that God is eternally existent. Some theorists take this to mean that God is timeless--categories of past, present, and future just do not apply when we are talking about God. Others hold, instead, that "eternal existence" means that God exists at all times. In other words, if God is eternally existent, he has already existed for an infinite amount of time, and he will continue to exist for an infinite amount of time--his existence never began and will never end.
About the latter concept of eternity, it is common to observe that we finite human beings cannot really conceive of the infinite. If that were the case, then we could not understand what God's eternity was; an eternity is an infinite amount of time. But others say we have some notion of an infinity--of at least a potential infinity. The idea is that we do have the notion of a series that begins and has not ended. A series of moments that has begun and not ended is potentially infinite.
Related to the notion of eternal existence is the concept of God as Creator, as a being completely independent of "everything else" that exists because he created everything else. (Contrast this with panentheism.) If this premise is true, than it follows that God is independent of both space and time, since these are properties of the universe. So according to this notion, God exists before time began, exists during all moments in time, and would continue to exist if somehow the universe and time itself were to cease to exist.
See also the nature of God in monotheistic religions.
Afterlife is often believed to be eternal.God and eternity