Exodus 33:4, 6 And when the people heard these evil tidings, they mourned, and no man did put on him his ornaments. And the children of Israel stripped themselves of their ornaments by the mount Horeb.
The people heard the bad news: God said He would not go up with them; He would send an angel before them instead. Their response: they mourned. They were saddened by this news. The God who had been with them could not be with them for the stiff-necked people would be consumed. They mourned in repentance as they realized that it was their unbelief that caused a separation: they could not go up without God. Separation is death; death is a separation. How could they go on without God?
Then they did not put on their ornaments. God said He would come in their midst and consume them, so they put off their ornaments. Putting off ornaments was an outward sign of inward repentance. The people instinctively knew that without God they were as good as dead. They responded by doing what God said and symbolically getting rid of anything getting between them and God.
We, too, need to fear that our sins would prevent the presence of the Lord from dwelling with us. We follow up repentance with tangible fruit, and because of Christ God will be with us. When the Lord threatens to withdraw His presence, His life, His peace, His protection, and His joy from us we repent, believe, and live. We respond to bad news by repenting and to good news by believing. Jesus is our Immanuel, God with us.