"Aslan," said Lucy, "you're bigger."
"That is because you are older, little one," answered he.
"Not because you are?"
"I am not. But every year you grow, you will find me bigger."
C. S. Lewis, The Chronicles of Narnia Book 4: Prince Caspian (Harper Collins, NY: 1979), 148.
Lewis' understanding of the Christian faith coupled with his ability to communicate through the written word place him in a unique category of authors from the time of Christ to the present day. He wrote many other works besides the Chronicles of Narnia including The Screwtape Letters and Mere Christianity. The Narnia Chronicles are perhaps his most well-known and are loved by a vast audience, Christian and non alike.
The non-Christian can certainly enjoy these works simply from a literary standpoint, as can the Christian. However, the real beauty of the books is that there weren't simply written to be a fanciful story, but rather an allegory. Lewis used the characters and worlds found in Narnia to tell the story of redemption. Aslan, the majestic and kingly lion is a type of Christ. In every book Aslan is portrayed the same, with his attributes paralleling the attributes of our Creator God.
Lucy, the youngest, has child-like faith (which is necessary to enter the world of Narnia). She was the one who first told the others about it back in The Lion, the Witch, and the Wardrobe. Thus, we see her as a Christian. In the aforementioned work (book 2 in the chronicles set) the four Sons and Daughters of Adam ascend the throne of Cair Paravel and rule for the Golden Age of Narnia. Then, as if no time had passed at all, they were drawn back to the wardrobe by the lamp post and when they came out in England they were children again, despite spending decades as the benevolent monarchs they were in Narnia.
Fast forward to Prince Caspian and a year has elapsed in England, but hundreds, if not thousands of years have passed in Narnia and once again the children are needed. My apologies if this spoils anything for you. There are still bountiful riches to be had to read them through to this point. All this is stated to get us to the quotation above. For Lucy, who first came to Narnia a year and a lifetime ago, her faith in Aslan has only grown. She hasn't laid eyes on him in perhaps 80 years (her time as queen plus her year in England), but she has never wavered in her faith. Now, when she sees him again he is bigger.
Aslan's answer that he does not grow old or bigger is a nod to the eternality and immutability of God. Aslan simply does not change just as God never changes or grows old. He has no beginning and no end; He is the Ancient of Days, the Alpha and Omega. For the Christian who believes in God and in Jesus Christ His Son through the revealed Word of the Bible, the longer we are in Christ, growing in the Word, growing in faith, the bigger God becomes, not because He has changed, but because we have grown in our understanding of Him.
This is the joy of the Christian life. If you do not know the joy of seeing God, through Christ, ever increase before you as you study the Word and increase your faith, then let me encourage you to spend more time in the Word, more time in prayer, and more time simply meditating on the goodness of God, so that He may ever increase (cf. Jn. 3:30)!