You shall not make for yourself an idol, or any likeness of what is in heaven above or on the earth beneath or in the water under the earth. You shall not worship them or serve them ... (Exodus 20:4-5A)
Because he regarded these verses to be explanatory of verse 3 rather than a separate commandment, Luther provided no explanation of these verses as such. In this Commandment we are forbidden to worship things – statues, pictures – as either gods or as representations of gods. Not even as representations of the true God or His heavenly creatures! God understands His creatures and our tendency to reduce our devotion to focus on tangible things, which are just created things. God doesn't want us worshiping false gods we have fashioned from things He created. If it's an insult to Him, it's all the more silly for us to be worshiping a creature as if it were the Creator. Nor does God want us reducing Him, in our minds, to something smaller that we ourselves are.
What does it mean to, “worship them or serve them”? The easy answer would be anything of our heart that should go to God. And that would be true, though not really all that useful as an explanation. Expressions acknowledging supreme worth (praise) belong to God. Expressions acknowledging sovereign power and authority (worship) belong to God. Expressions of total trust and reliance (prayer) should only be addressed to God. The unqualified loyalty of our whole being belongs only to God. Our things, our career, our family, even ministries we might work in are subsidiary to and have their validity in God. Even things such as “lucky (name of item)s” are expressions of a trust that belongs to God.