The words "eternal" and "everlasting" both mean the same thing. But for us to understand them can be quite difficult. We think of something that is everlasting as going on and on for ever. In a sense that is quite true. But in Psalm 90 we read that God is described as being "from everlasting to everlasting." That means that there never was a time when God did not exist — he is the eternal God, the Creator who brought all things into being, including time itself. So God is not affected by time; he is always present. Eternal (or everlasting) is a word that uniquely belongs to God.
When Jesus Christ said "this is life eternal, that they (those believing in him as Saviour) may know you, the only true God, and Jesus Christ whom you have sent," the eternal life he referred to was a special kind of life.
Not only does this special life last for ever and ever, it starts here and now when a person comes to trust in Jesus as his/her Saviour. And not only so but it has a special quality — it has something of the very life of God himself in it so that when a believer in Jesus dies, he/she will immediately go into the very presence of God to enjoy this eternal life in a fuller way that will be pure joy, holiness and perfect praising — fitted for the presence of God himself.
Dear Lord Jesus, I thank you for the gift of everlasting life. Amen.