Memorizing new Bible verses makes you repeat, rehearse, and go over the words multiple times. This makes you notice things that you might normally gloss over while simply reading. I’d say this is one of the reasons that it is good to hide God’s Word in our hearts (Psalm 119:11).
Throughout the Bible we can see that it has been good for people to know God’s Words, and through personal life experience we can know this as well. When you discover “new” things in the Bible, you don’t always just learn something new to your experience or deeper to your knowledge of God. You might find something that you need just at that moment. You might find something you will need in the future. You might find something to help you reconcile the past. You might find something to encourage another person. You might find… conviction.
But no matter what it is that you find or gather from your memorization of the Bible, God has a very good reason for putting it there and leading you to it at that point. If you don’t already or if you’ve stopped, I would certainly recommend continually memorizing, and thereby learning, more of the Bible, and reviewing what you’ve already memorized and learned.