In the presence of God, the glory of God (what one sees of the presence of God) was transferred to Moses so that his face shown radiant.
I have no clue what that looked like – but it was a sight sufficiently foreboding that it scared Aaron and all the leaders of Israel (Exodus 34:29ff). Had it been me, I would have been tempted to cover my face so it wouldn’t be so scarey. But Moses took the opposite tact. Moses covered his face after he spoke to Israel.
Why?
So they would not see the glory of God fading from him. As long as his face was radiant, all Israel knew that he stood approved and empowered by God. Moses did not want Israel to see that, over time, the radiance faded.
Paul’s point in chapter three is that the ministry of the new covenant, Christianity, is so superior to the old, that the glory of God in its recipients should not fade, but grow more obvious every day.
Often we think of our conversion, or the moment of our salvation, as the high point of our religion – just as Sinai was the high point for Israel. But it’s not supposed to be that way. We are called to be transformed into the likeness of Christ with ever-increasing glory, and this all is made possible by the Spirit of God.
Do you see Paul’s point? The lives of Christians must change, and for the better, as time goes on. This is the sign of a growing relationship with God. The change must be seen in improving behavior. Christians have other options, but none of them are viable.