I've already provided some much more detailed commentary from Zacharias Ursinus on the second commandment (link to commentary). The following selections are taken from Ursinus' Large and Small Catechisms, respectively. A harmony of Ursinus' catechisms and the Heidelberg Catechism can be found here (link). It's worth noting that Ursinus was an author of the Heidelberg catechism (which we examined at this link) as well.
Ursinus' Large Catechism
163 Q What is the second commandment?
A “You shall not make for yourself a graven image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth; you shall not bow down to them or serve them; for I, the Lord your God, am strong and jealous visiting the iniquity of the fathers upon the children to the third and the fourth generation of those who hate me, but showing steadfast love to thousands of those who love me and keep my commandments.”
164 Q What is the meaning of this commandment?
A That we not try to worship God in any other way than he has commanded in his Word.
165 Q But are all sculptured or painted images forbidden by this law?
A No, only those which are made to portray or worship God.
166 Q Why doesn’t God want to be portrayed by a visible form?
A Since he is eternal and incomprehensible Spirit, every representation of him in a corruptible, lifeless, bodily form, is a lie against God and diminishes his majesty.
167 Q What does it mean to worship God through images?
A It means to turn, whether in soul or body, to images when worshiping God, as if God would listen to us better if he were worshiped through them; or to show honor to them by thought, gesture, mention of the divine name, or any external sign whatsoever as if they represented God; or to desire in any way to worship God by using them.
168 Q Why is it improper to worship God with images?
A Because it is not for any creature but for the divine authority alone to institute the form of divine worship and the signs of the divine presence. To represent God differently than he is, is a serious insult to him.
169 Q Why does God forbid not only worshiping but even making such images?
A So that we don’t appear to approve of idolaters by having these images which can be a form of, or the occasion for idolatry. And so that we don’t put God to the test by giving occasion for anyone else to sin.
170 Q Then this commandment isn’t just talking about images?
A No, not only about images but also all humanly devised worship of God.
171 Q Why does God add a threat and a promise to this commandment?
A So that he may all the more effectively frighten us away from idolatry, one of the worst of sins.
172 Q Why does he call himself “strong”?
A So that we fear his power for vengeance.
173 Q Why “jealous”?
A Because he never allows his honor to be given to another without punishment on account of the greatness of this sin.
174 Q Why does he threaten punishments even for the descendants of sinners?
A First, so that he may show the greatness of this sin which would bring down punishment, not only on those who commit it, but also on their descendants if God desired to act according to his strict justice. Second, so that people at least out of concern for their descendants, will keep themselves from sin.
175 Q But does the justice of God permit the descendants to be punished for the sins of their parents?
A Yes. For we have such a corrupt nature that we would all continue in the sins of our parents if God did not look on us with his matchless mercy.
176 Q Why does he promise to bless the descendants of the upright?
A First, so that he might express the greatness of his mercy to the upright by which he not only deals kindly with them but also with their descendants, and also so that he might move us more to thankfulness and zeal for his honor. Second, so that he might draw us to godliness through the happiness promised to our descendants.
177 Q Then do all the descendants of the upright receive mercy from God?
A By this promise God did not bind his grace to the physical descendants, but he did distribute both spiritual and physical blessing to the descendants of the upright as he saw fit to do from eternity in order to show forth his glory.
178 Q Why does he say that he will show kindness to thousands of generations and will punish four?
A To show that he rejoices not in the damnation but in the salvation of men, and that he punishes only as a demonstration of his justice.
Ursinus' Small Catechism
84 Q What does the second commandment require?
A That we earnestly desire to worship God, not by our own will, but only by the command of the divine Word – in spirit and in truth, so that we do not, by false and idolatrous worship, bring terrible punishments upon ourselves and our descendants.
85 Q Then does God forbid the making or keeping of all images?
A No, only those which are made to represent or worship God or which give an occasion for or the appearance of idolatry.
86 Q But shouldn’t images be permitted in Christian churches as teaching aids for the unlearned?
A No, God certainly does not want his church to be taught by images and statues but by his Word. Therefore, those who dare to add statues to this aspect of divine worship, sin against this commandment and do not escape the guilt of idolatry.