Question: "What does it mean for a Christian to grow in faith?"
Answer: We are commanded in Scripture to "grow in the grace and knowledge of our Lord and Savior Jesus Christ" (2 Peter 3:18). This growth is spiritual growth, growing in faith.
At the moment we receive Christ as our Savior, we are born again spiritually into God's family. But just as a newborn baby requires nourishing milk for growth and good development, so also a baby Christian requires spiritual food for growth. "Like newborn babies, crave pure spiritual milk, so that by it you may grow up in your salvation, now that you have tasted that the Lord is good" (1 Peter 2:2-3). Milk is used in the New Testament as a symbol of what is basic to the Christian life.
But as a baby grows, its diet changes to also include solid foods. With this in mind, read how the writer of Hebrews admonished the Christians: "In fact, though by this time you ought to be teachers, you need someone to teach you the elementary truths of God's word all over again. You need milk, not solid food! Anyone who lives on milk, being still an infant, is not acquainted with the teaching about righteousness. But solid food is for the mature, who by constant use have trained themselves to distinguish good from evil" (Hebrews 5:12-14). Paul saw the same problem with the Corinthian believers; they had not grown in their faith, and he could only give them "milk" because they were not ready for solid food (1 Corinthians 3:1-3).
The analogy between a human baby and a spiritual baby breaks down when we realize how each baby matures. A human baby is fed by his parents and growth is natural. But a baby Christian will only grow as much as he purposefully reads and obeys and applies the Word to his life. Growth is up to him. There are Christians who have been saved many years, but spiritually they are still babies. They cannot understand the deeper truths of the Word of God.
What should a Christian's diet consist of? The Word of God! The truths taught in the Bible are rich food for Christians. Peter wrote that God has given us everything we need for life through our (growing) knowledge of Him. Read carefully 2 Peter 1:3-11 where Peter lists character qualities that need to be added to our beginning point of faith in order for maturity to take place and to have a rich welcome into the eternal kingdom of our Lord and Savior Jesus Christ.