But whenever a person turns [in repentance] to the Lord, the veil is stripped off and taken away. ...And all of us, as with unveiled face, [because we] continued to behold [in the Word of God] as in a mirror the glory of the Lord, are constantly being transfigured into His very own image in ever increasing splendor and from one degree of glory to another; [for this comes] from the Lord [Who is] the Spirit. (2 Corinthians 3:16-18 AMP)
Moses used to wear a veil so the people of Israel wouldn't be bothered by the glow on his face. It was the glow of the glory of spending time with the Lord. The Israelites were uncomfortable with the Lord's presence, afraid mainly.
But when Moses wanted to talk to God he went into the Tabernacle and took the veil away so that he and the Lord could speak as friends speak. When we are young and as we grow older we have a veil over our face that prevents the understanding of God. But if we turn away from sin and towards Him that veil is taken away. Then we can talk to God as a friend like Moses did.
Because the veil is shed, we can read God's word and understand God and each day we shine more and more. This is not because we learn more rules from the Bible but because we become nearer and nearer to our Savior. Not only nearer but He even creates in us a heart more like His.