Answer: God wants believers to be conformed to the likeness of His Son. Jesus then becomes the firstborn--the eldest, the One with the highest honor--in the family of God, (verse 29). Believers--those in the family of God who are sons of God--conform to, imitate, copy, emulate, the eldest Son, Who is God's firstborn.
MORE INFORMATION AND/OR OTHER SCRIPTURE REFERENCES:
Romans 12:2: "Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God's Will is--His good, pleasing and perfect Will."
1 Corinthians 2:16: "‘For who has known the mind of the Lord that he may instruct Him?' But we have the mind of Christ."
2 Corinthians 3:18: "And we, who with unveiled faces all reflect the Lord's glory, are being transformed into His likeness with ever-increasing glory, which comes from the Lord, Who is the Spirit."
Philippians 3:20-21: "But our citizenship is in heaven. And we eagerly await a Savior from there, the Lord Jesus Christ, Who, by the power that enables Him to bring everything under His control, will transform our lowly bodies so that they will be like His glorious body."
1 Peter 1:14-16: "As obedient children, do not conform to the evil desires you had when you lived in ignorance. But just as He Who called you is holy, so be holy in all you do; for it is written: ‘Be holy, because I am holy.'"