Eternity is an endless span of time or an indefinite span of time. Having an endless lifetime after physical death is explained in the Bible.
John 003:016 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. 003:036 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him. 004:014 But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life. 005:024 Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life. 006:027 Labour not for the meat which perisheth, but for that meat which endureth unto everlasting life, which the Son of man shall give unto you: for him hath God the Father sealed. 006:040 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day. 006:047 Verily, verily, I say unto you, He that believeth on me hath everlasting life. 006:051 I am the living bread which came down from heaven: if any man eat of this bread, he shall live for ever: and the bread that I will give is my flesh, which I will give for the life of the world. 006:053 Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you. 006:054 Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day. 006:058 This is that bread which came down from heaven: not as your fathers did eat manna, and are dead: he that eateth of this bread shall live for ever. 011:025 Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: 011:026 And whosoever liveth and believeth in me shall never die. Believest thou this? 012:025 He that loveth his life shall lose it; and he that hateth his life in this world shall keep it unto life eternal. 014:002 In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you. 014:003 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also. 017:002 As thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him. 017:003 And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. 1 John 002:016 For all that is in the world, the lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world. 002:017 And the world passeth away, and the lust thereof: but he that doeth the will of God abideth for ever. 002:025 And this is the promise that he hath promised us, even eternal life. 003:002 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is. 005:011 And this is the record, that God hath given to us eternal life, and this life is in his Son. 005:012 He that hath the Son hath life; and he that hath not the Son of God hath not life. 005:013 These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God. 005:020 And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life. Romans 002:006 Who will render to every man according to his deeds: 002:007 To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life: 005:021 That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal life by Jesus Christ our Lord. 006:023 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord 008:011 But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you. Titus 001:002 In hope of eternal life, which God, that cannot lie, promised before the world began; 1 Corinthians 015:051 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, 015:052 In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed. 015:053 For this corruptible must put on incorruption, and this mortal must put on immortality. 015:054 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory. 1 Timothy 006:011 But thou, O man of God, flee these things; and follow after righteousness, godliness, faith, love, patience, meekness. 006:012 Fight the good fight of faith, lay hold on eternal life, whereunto thou art also called, and hast professed a good profession before many witnesses. Hebrews 005:009 And being made perfect, he became the author of eternal salvation unto all them that obey him; Daniel 012:002 And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt. 012:003 And they that be wise shall shine as the brightness of the firmament; and they that turn many to righteousness as the stars for ever and ever.