Abiding in Christ is the source of the abundant life Jesus spoke of in John 10:10. Those who abide fulfill the magnificent purpose of life, which is to give God the glory He deserves. Jesus said in verse 8, "My Father is glorified by this, that you bear much fruit." When a Christian abides, God can work through him to produce much fruit. Since God produces it, He is the one glorified.
Paul recognized the source of fruit in his life. He said in Romans 15:18, "For I will not presume to speak of anything except what Christ has accomplished through me." He did not tell people how good he was at preaching or evangelism. He recognized that everything worthwhile in his life came from God.
In Galatians 2:20 he said, "I have been crucified with Christ; and it is no longer I who live, but Christ lives in me." He knew God accepted the ransom of Jesus Christ and allowed Jesus to sit next to Him to be a mediator between Him and man.
Giving ourselves over to Christ Jesus can work for us and be the one presenting ourselves to God in the best way a solicitor or barrister can do. Assured of the one mediator for us we can work at ourselves to become like Christ, also only wanting to do the Will of God, like Jesus did not do his will but the Will of his heavenly Father.
With our effort to become like Christ we can only try to do our best to become righteous in the eyes of God and to show others that we are not part of this world but part of Christ's Body unto the glory of the heavenly Father, the God of Jesus, Who is the God of Abraham, the God of Isaac and the God of Jacob, founder of the world..
Peter had the same idea in mind when he said in 1 Peter 2:12, "Keep your behavior excellent among the Gentiles, so that in the thing in which they slander you as evildoers, they may because of your good deeds, as they observe them, glorify God in the day of visitation."
So this is the logical progression: the one who abides bears fruit; God is glorified in the fruit because He is the One who deserves credit for it; the purpose of life is fulfilled because God is glorified; and thus the one who abides and glorifies God experiences abundant life.