These Israelites learned religion from the Egyptians who, like all other cultures, worshiped corporeal forms of deity, idols. While the Israelites did believe in an incorporeal God they clung to the notion that a concrete, tangible link is required.
In the Israelites' experience, the Divine presence often dwelled in tangible, or at least visible, symbols and artifacts. At the Red Sea it was Moses' staff, at Sinai it was a cloud of glory, in the tabernacle it would be a sacred ark and its extending cherubs. The people saw these as deified links between an incorporeal God and a physical people. God speaks from the cloud around Sinai, the High Priest approaches God in the Holy of Holies atop the ark, etc.
After their Sinai experience, the people looked to Moses as the primary intermediary. When God uttered the commandments, the people found the experience overwhelming. They asked Moses to stand as their intermediary and transmit God's message to them. They saw Moses as a link to the true God, creator of heaven and earth. When Moses did not return from the mountain they feared their link to God was severed. They panicked and wanted to replace Moses.
When the people saw how long it was taking Moses to come back down the mountain, they gathered around Aaron. "Come on," they said, "make us some gods who can lead us. We don't know what happened to this fellow Moses, who brought us here from the land of Egypt." So Aaron said, "Take the gold rings from the ears of your wives and sons and daughters, and bring them to me." All the people took the gold rings from their ears and brought them to Aaron. Then Aaron took the gold, melted it down, and molded it into the shape of a calf. When the people saw it, they exclaimed, "O Israel, these are the gods who brought you out of the land of Egypt!" - Exodus 32:1-4 NLT
When they thought Moses died, it appeared crucial that a replacement be found. Without one there would be no further access to God and no method of securing his grace. But this time they sought a physical object rather then a living human. Physical objects, they reasoned, can be safely preserved; they don't walk away and disappear as Moses did.
Why use the image of a calf to replace Moses as their conduit to God?
In both Egyptian and Canaanite cultures the bull or calf directly represents a deity — usually a storm god. At other times it represents the deity’s mount, signifying the deity indirectly. In other words, they did not intend the calf to depict YHVH but to function as the conduit of His presence among them, as Moses had functioned previously. Many scholars believe that the calf did so by serving as the pedestal or mount on which YHVH was invisibly present, as did the cherubs in the Holy of Holies.
Regardless of their intentions, with the making of this image they violated the second commandment and the situation quickly descended into idol worship in violation of the first commandment. It has been little more than a month since the commands where given by God Himself, His fiery presence is still on the mountain above them but here they are in willful disobedience in the very presence of God.
Aaron saw how excited the people were, so he built an altar in front of the calf. Then he announced, "Tomorrow will be a festival to the LORD!" The people got up early the next morning to sacrifice burnt offerings and peace offerings. After this, they celebrated with feasting and drinking, and they indulged in pagan revelry. The LORD told Moses, "Quick! Go down the mountain! Your people whom you brought from the land of Egypt have corrupted themselves. How quickly they have turned away from the way I commanded them to live! They have melted down gold and made a calf, and they have bowed down and sacrificed to it. They are saying, 'These are your gods, O Israel, who brought you out of the land of Egypt.'" - Exodus 32:5-8 NLT
Remember how Moses responded to God’s calling at the burning bush? He did not want anything to do with these people and here is his chance to leave it all behind. How does Moses respond to God giving him the out he wanted back at the burning bush?
Then the LORD said, "I have seen how stubborn and rebellious these people are. Now leave me alone so my fierce anger can blaze against them, and I will destroy them. Then I will make you, Moses, into a great nation." But Moses tried to pacify the LORD his God. "O LORD!" he said. "Why are you so angry with your own people whom you brought from the land of Egypt with such great power and such a strong hand? - Exodus 32:9-11 NLT
Moses left the burning bush as a very reluctant messenger but in just three short months God has given to him a love for God’s chosen people and a fearless nature, zealous for God.
When Aaron began his story he was a willing spokesperson for Moses on God’s mission but while he could stand against Egypt he could not stand against his people. He offered no resistance to their rebellion and fashioned their calf, and when Moses returned he sought to pass the blame onto the calf itself.
Finally, he turned to Aaron and demanded, "What did these people do to you to make you bring such terrible sin upon them?" "Don't get so upset, my lord," Aaron replied. "You yourself know how evil these people are. They said to me, 'Make us gods who will lead us. We don't know what happened to this fellow Moses, who brought us here from the land of Egypt.' So I told them, 'Whoever has gold jewelry, take it off.' When they brought it to me, I simply threw it into the fire--and out came this calf!" - Exodus 32:21-24 NLT
Levi began with his mother seeking attachment to her husband in a loveless marriage and lost his temper out of attachment to his sister. But here Levi redeems himself and is now ordained for the Lord’s service and will be forever attached to God’s service as priests.
Moses saw that Aaron had let the people get completely out of control, much to the amusement of their enemies. So he stood at the entrance to the camp and shouted, "All of you who are on the LORD's side, come here and join me." And all the Levites gathered around him. Moses told them, "This is what the LORD, the God of Israel, says: Each of you, take your swords and go back and forth from one end of the camp to the other. Kill everyone--even your brothers, friends, and neighbors." The Levites obeyed Moses' command, and about 3,000 people died that day. Then Moses told the Levites, "Today you have ordained yourselves for the service of the LORD, for you obeyed him even though it meant killing your own sons and brothers. Today you have earned a blessing." - Exodus 32:25-29 NLT
Originally, the firstborn of Israel were intended to serve God after He saved them from the plague that killed all of the firstborn sons in Egypt (Exodus 11). When the firstborns participated in the sin of the Golden Calf in the desert (Exodus 32), they disqualified themselves from serving in the Jewish Temple. The tribe of Levi (the tribe of Moses and Aaron) refrained from the sin, so they took the place of the firstborns, serving in the Tabernacle and later in the Temple as musicians, guards, and in several other roles.
It will take further intercessory prayer from Moses for the people to gain the forgiveness of God for this crime. Without the prayers of Moses they would have been wiped out in the desert. Without the work of Jesus we would be wiped out, guilty in our sins.
We need to remember that we can go directly to God; we don’t need an intermediate object or person.
We need to remember that even in sin and judgment there is redemption.
We need to remember that the world needs us to pray like Moses for them.