Eternal life is the promise from God that we are saved from sin, death and separation from him. We can have hope in the promise because the one who made the promise is able to keep that promise.
This is the crux of Christianity, we can trust the one who has made us promises. Problems arise when you don't know what he's promised. Debates arise over what he actually has promised.
We know for sure that God has promised eternal life to all those who come to him in the name of Jesus Christ, by grace through faith. So we can rest assured that we can hope for (confidently expect) to live with God, in God, for all eternity in a perfect place, the restored Eden, Heaven.