The Father uses those He's given to Christ to glorify Him. Jesus uses the verb gives 17 times in this prayer and 13 of those times refer to the Father giving to the Son (John 17:2).
John 17:6 says, "I have manifested Your name to the men whom You gave Me out of the world; they were Yours and You gave them to Me, and they have kept Your word."
Verses 9-10 say, "I ask on their behalf; I do not ask on behalf of the world, but of those whom You have given Me; for they are Yours; and all things that are Mine are Yours, and Yours are Mine; and I have been glorified in them."
Here Jesus claims to share everything with the Father. He is pleading for His sheep, the ones the Father has already given Him. Jesus cares about His sheep because the Father gave them to Him. And that gift, those given to the Son, was sealed when Christ purchased them with His blood.
Verse 10 says, "All things that are Mine are Yours."
Jesus is saying the Father has chosen these individuals before the foundation of the world.
In Ephesians 1:3-6, Paul says, "Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption to himself as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace, with which he has blessed us in the Beloved."
This doesn't just refer to the apostles but to all who come to faith in Christ. Before the foundations of the world, God gave people to Jesus as a gift, and Jesus openly embraces them, giving them eternal life.
Knowing hostile Jews meant him harm, Paul may have doubted God had chosen any of the Corinthians, but Jesus assured him, in Acts 18:9-10, "Do not be afraid, but go on speaking and do not be silent, for I am with you, and no one will attack you to harm you, for I have many in this city who are my people."
God assured the apostle that there were people in Corinth who had yet to hear and respond to the gospel message yet were, indeed, His people. Even though they hadn't repented and believed, they were His. The Father gave them to Christ before the foundations of the world.
Some people believe God chose those He knew would come to Him of their own volition. If that were the case, then God's plan of salvation would depend on us. That would mean grace is no longer grace and God is not fully sovereign. Apart from the gospel, apart from God changing our nature, apart from Him turning our heart of stone into a heart of flesh, that's impossible. We cannot believe in God apart from Him doing a work in us.
Charles Spurgeon suggested several reasons it's important that we know this.
We cannot save ourselves.
It is Christ who saves us. Therefore, we have no grounds to boast. Instead, we can only boast in the Lord (1 Corinthians 1:26-31).
Jesus treasures those given to Him.
On a recent trip to Walmart to mark a milestone in our daughter's life, she chose one item after another, putting back the one previously chosen—until she saw a stuffed puppy. She had to have that puppy. Unlike many toys in our home, those she plays with occasionally and shares readily, this stuffie does not leave her side. She loves and treasures it.
In a similar way, Jesus treasures everyone the Father gave Him—so much so that He purchased our salvation with His blood. He didn't die for us because of our innate worth. He died for us because He values us. He loves all believers because the Father gave us to Him and we're His.
Nothing is truly about us.
First Corinthians 6:19-20 says, "Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own, for you were bought with a price. So glorify God in your body."
While Paul is referring to sexual purity, the truths of this passage apply to all aspects of life. We belong to God. Because He dwells within us, we must keep ourselves morally pure.
It's not our money, our house, or our car. In fact, ultimately, our sons and daughters aren't ours. Everything we have has been given to us as a gift, so we can spread the gospel throughout the world. Because we're not our own, we should seek to glorify Christ at all times.
How do we glorify Christ? By living for Him and displaying the fruit of the Spirit. He is glorified when we trust Him. He is glorified when we find our joy in Him. He is glorified when we tell others about Him. And He is glorified when others see us trusting Him. 
May we seek to glorify Him this day—and every day!
 Based on C. H. Spurgeon, Metropolitan Tabernacle Pulpit [Pilgrim Publications], 510-513