Why did God give His people the Ten Commandments?

God gave rules to show how to love Him and others. 

God made a covenant with His people: If you obey Me, you will be My people. (Exodus 19:5-6)  But the people did not obey God. They sinned against God, and Moses asked God to forgive them. Moses acted as their mediator, or advocate, before God. When we sin, Jesus is our Mediator. Through Jesus, we can be forgiven of our sins. God is then pleased with us, because He looks at Jesus, who never sinned.