Where this story begins: Exodus 20
"I am the LORD your God, who brought you out of Egypt, out of the land of slavery. You shall have no other gods before me. You shall not make for yourself an idol in the form of anything in heaven above or on the earth beneath or in the waters below."
Let's study what this means, shall we? This is the LORD proclaiming His name and His glory. He says there should be no other god. He then says to not make an idol. He is not being redundant here, he is giving two orders. The first is obvious, have no other gods. The second is to make no physical representation of God. Let's travel further to Exodus 32.
"When the people saw that Moses was so long in coming down from the mountain, they gathered around Aaron and said, "Come, make us a god who will go before us. As for this fellow Moses who brought us up out of Egypt, we don't know what has happened to him."
Aaron answered them, "Take off the gold earrings that your wives, your sons and your daughters are wearing, and bring them to me." So all the people took off their earrings and brought them to Aaron. He took what they handed him and made it into an idol cast in the shape of a calf, fashioning it with a tool. Then they said, "This is your god, O Israel, who brought you up out of Egypt."
When Aaron saw this, he built an altar in front of the calf and announced, "Tomorrow there will be a festival to the LORD."
The golden calf represented something, it represented the LORD, as Aaron invoked the name of the LORD, and the Israelites referenced, as God did, the deliverance from Egypt. But it seems more difficult than this. It seems as if Aaron was using this idol as a way to keep the Israelite's allegiance to the LORD and the Israelites wanted to give glory to a different god.Both of the first commandments were broken in this way at this time.