Exodus 34 is a chapter of restoration. God commands Moses to cut new tablets, and He Himself writes the same covenant words again. The broken covenant is renewed not because Israel has improved, but because of God's character. When Moses asked to see God's glory (33:18), God answered by proclaiming His name.
Yahweh! Yahweh, a merciful and gracious God, slow to anger, and abundant in loving kindness and truth, keeping loving kindness for thousands, forgiving iniquity and disobedience and sin; and who will by no means clear the guilty (34:6-7). This is one of the most quoted passages in the Old Testament (Numbers 14:18; Nehemiah 9:17; Psalm 86:15; Joel 2:13). It holds together God's overflowing mercy and His perfect justice. Christians have read this as meeting at the cross, where God is just and also forgives (Romans 3:26).
God renews the covenant with promises of wonders and warnings against idolatry, for His name is Jealous (34:14). This is not petty envy, but the rightful love of a husband for his bride. Moses' forty days of fasting and his shining face show the effect of being near God's glory. In the New Testament, Paul explains that Moses' veil hid a fading glory, but in Christ the veil is removed, and believers with unveiled faces are transformed from glory to glory (2 Corinthians 3:7-18).