In Colossians 1:9, Paul says he prays that the Colossian believers would be "filled with the knowledge of [God's] will." The reason for this is so that they would be able to "walk in a manner worthy of the Lord." In other words, Paul says we need to know the will of God in order to live the kind of life God wants us to live. You can't obey what you don't know.
The goal of the Christian life is to be "fully pleasing to him" (Colossians 1:10), and in order to please someone, you need to know what pleases them. This is one thing that is meant by "the knowledge of God."
God's desire is that Christians would grow in the knowledge of God so that we can please Him. This is linked to "bearing fruit in every good work" (Colossians 1:10). You can’t bear godly fruit if you don’t know God’s will, and you won’t grow in the knowledge of God if you’re not committed to bearing fruit.
There's Knowledge, and Then There's Knowledge
This is because the knowledge of God is not a dry understanding of true statements. It isn’t answering questions about God correctly. Even the devil can do that. The knowledge of God certainly includes that: you can’t separate truths about Christ from Christ. If you want to know Him, you can’t conjure up your picture of Him and worship that image. You have to go to the Word, discover who He really is, and worship Him. We discover who God is, and what pleases Him in the pages of the Bible.
There’s a relationship between knowing Christ and obeying Christ. The more you know Him, the more you ought to obey Him, and the more you obey Him, the more you get to know and be like Him. In other words, a real knowledge of God will lead to good works which, in turn, will lead to an even greater knowledge of God. One example of this would be in the act of forgiveness. We know the will of God is that we would forgive as our Heavenly Father has forgiven us (Matthew 6:14). Therefore, to do the will of God means to actually forgive those who have sinned against us. So far so good. But notice what happens when you actually start practicing forgiveness: you in turn grow in the knowledge of God. How so? Because you start to experience first hand just what it means to forgive someone else, and you can't truly understand what God has done for you in forgiveness if you don't practice it yourself.
In other words, you know the will of God is to forgive. You do the will of God by forgiving. As you forgive others, you develop a deeper understanding of what God did for you in forgiving you. You grow in the knowledge of God.
Fruit and Multiplication
The reference to bearing fruit and increasing occurs twice in Colossians 1, in verses 6 and 10. This echoes the first mandate given to the first human beings in Genesis 1:28, to be fruitful and multiply. In Colossians, Paul says that one of the things that multiplies, one of the things that should increase, is the knowledge of God in the lives of believers. Habakkuk 2:14 says something similar:
For the earth will be filled with the knowledge of the glory of the LORD as the waters cover the sea.
Everyone who goes on ahead and does not abide in the teaching of Christ, does not have God. Whoever abides in the teaching has both the Father and the Son. If anyone comes to you and does not bring this teaching, do not receive him into your house or give him any greeting, for whoever greets him takes part in his wicked works.
“If the standard level of what is done in a worship service is set at that which the newest, least-informed Christian can understand, we are doomed to remain forever in spiritual infancy. As Christians, we should expect worship to always be a learning experience.”