What It's Not
Eternal life is frequently confounded with eternal existence and immortality, but it is not either of these. All people will eternally exist, but not all have eternal life, because that is God's gift to believers only (John 3:36). Unbelievers "shall not see life," yet they will exist, for it is added, "The wrath of God abideth on him." Nor is eternal life the same as immortality. God alone has immortality as an independent possession of self-existence (1 Timothy 6:16). Subordinately angels, too, are immortal (Luke 20:36). Immortality when applied to believers refers alone to the body when it will be raised or changed (1 Cor. 15:53,54). Need we add that the soul of man is immortal, although the word is not applied to it in Scripture.
Eternal life, therefore, is necessarily distinct from both eternal existence and immortality. Neither angels nor unbelievers are said to have eternal life, though the former are immortal, and the latter eternally exist.
What It Is
How is eternal life received? It is the gift of God (Romans 6:23) through Jesus Christ (John 10:28), given to all who believe on Him for salvation (1 John 5:13). All believers have eternal life, both in the Son as its source (John 1:4; 1 John 5:11), and in believers as derived from and dependant upon Him (1 John 5:12).
That eternal life is actually and positively in believers is very simply shown by our Lord in John 15:4,5. Christ is the vine, and believers are the branches, in whom the life of the vine is the life and power for bearing fruit. The source of life for us is the Son, and we have it from Him and in ourselves (see John 6:53,54) Again, in 1 John 3:15, the Bible speaks of sinners as not having eternal life abiding in them. This is in contrast to true believers, who do have it abiding in them.
Eternal life is rarely mentioned in the first three Gospels, and only then as a future thing (Matthew 25:46; Mark 10:30). Paul and John speak of eternal life as a matter of promise also (Titus 1:2; 1 John 2:25). Thus eternal life is spoken of as in us now, and also as future. Eternal life is needful for the soul's enjoyment of Christ and delight in all that is holy, good, and heavenly. When a soul is born of God, then he only and truly begins to live, and that is termed eternal life.
—Adapted from Doctrinal Summaries by Walter Scott.