Eternity (or forever) is endless time. It is often referenced in the context of religion, in the concept of immortality, whereby death is conquered, and people may live for an unlimited amount of time (cf. Heaven). The existence of gods or God is said to endure eternally and sometimes also the natural cosmos, in respect to both past and future.
By contrast, the concept of a mathematically infinite duration, is called sempiternity or everlasting. Whereas the eternal is said to be unchanging and outside time; a potentially sempiternal span of time can never come to pass in actuality. Aristotle argued that the cosmos has no beginning.
Eternity
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http://en.wikipedia.org/wiki/Eternity
Eternity
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http://plato.stanford.edu/entries/eternity/
Concepts of eternity have developed in a way that is, as a matter of fact, closely connected to the development of the concept of God in Western thought, beginning with ancient Greek philosophers; particularly to the idea of God’s relation to time, the idea of divine perfection, and the Creator-creature distinction. Eternity as timelessness, and eternity as everlastingness, have been distinguished. Following the work of Boethius and Augustine of Hippo divine timelessness became the dominant view. In more recent times, those who stress a more anthropomorphic account of God, or God’s immanence within human history, have favored divine everlastingness. The debate has been sharpened by the use of McTaggart’s distinction between A-series and B-series accounts of temporal sequence.