Now Jesus did many other signs in the presence of the disciples, which are not written in this book; but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.(John 20:30-31 ESV)
John wrote these things (his book) for a reason and he gives us that reason here at the end of chapter 20.
This is not a book about a vague God but a particular person, Jesus. It's a book that shows that Jesus is the Christ, the messiah, He is the culmination of God’s plan throughout history. It's book that tells us that Jesus is the Son of God, not just someone who tells us about God. God exists in a glorious loving community that pours love outwards towards us, the rebels who have rejected him.
This book was written so that we can have life - real life. Separation from the author of life is death, there is no life outside of him. This life is not an ethereal event in the future, but fulness of life now into eternity. It's a book that makes it clear that the way we can have this life is by believing in Jesus - not doing something, not following his example - simply believing that He is who He says He is. When we believe in Him, our life is in Him. We are in Jesus, we are as accepted and loved as he is, we are empowered by the same spirit he is, we are united in him, he is with us.