The Central Idea of the Text is that Israel breaks covenant with God through idolatry and Moses intercedes on their behalf.
The Israelites had turned away from the Lord and broken His covenant. They celebrated their disobedience with "a feast" and "play" and "singing" and "dancing" that angered the Lord, though it brought ephemeral happiness. In judgment, everyone was made to drink bitter water (Ex. 32:20), and it seems God's judgment fell hardest on those who led the rebellion (Ex. 32:27-28). Israel's history was at times marked by leaders who personally engaged in idolatry and led God's people to do the same (cf. 1 Ki. 11:6-10; 12:26-33; Ezek. 16).
Aaron's sin was that he surrendered to sinful pressures of the Israelites and built an idol for the people to worship. Moses prayed for Aaron, and the Lord spared his life (Deut. 9:20). Even though he failed like many others in the Bible (e.g. David, Elijah, Peter, etc.), Aaron went on to become a great servant of the Lord. This is grace.
Even though Israel was guilty of terrible sin, Moses advocated and sought the Lord's forgiveness on their behalf, citing covenant promises so that Israel would be spared the Lord's righteous anger (Ex. 32:11-13; cf. Deut. 9:18-19). God heard Moses' prayer and "changed His mind about the harm which He said He would do to His people" (Ex. 32:14). Moses shows commitment-love toward Israel by seeking the Lord's interest on their behalf, even though they didn't deserve it. Moses revealed he was willing to die with his people if the Lord would not forgive, and this says something about his character as a godly leader (Ex. 32:31-32).
The Christian is to live by faith in God and guard himself from idols (1 John 5:21). Idolatry can bring ephemeral happiness and worldly pleasure, but it will also bring the Lord's judgment upon those who break covenant with Him (Heb. 12:5-11).
