The potter and clay imagery is found several places in the Bible.

Isa 29:16 Surely you have things turned around! Shall the potter be esteemed as the clay; For shall the thing made say of him who made it, “He did not make me”? Or shall the thing formed say of him who formed it, “He has no understanding”?

Isa 41:25 “I have raised up one from the north, And he shall come; From the rising of the sun he shall call on My name; And he shall come against princes as though mortar, As the potter treads clay.

Isa 64:8 But now, O LORD, You are our Father; We are the clay, and You our potter; And all we are the work of Your hand.

Jer 18:6 “O house of Israel, can I not do with you as this potter?” says the LORD. “Look, as the clay is in the potter’s hand, so are you in My hand, O house of Israel!

Lam 4:2 The precious sons of Zion, Valuable as fine gold, How they are regarded as clay pots, The work of the hands of the potter!

Rom 9:21 Does not the potter have power over the clay, from the same lump to make one vessel for honor and another for dishonor?

The imagery of a potter and clay suggest someone who molds and someone who is molded. There is an implicit subservient relationship implied throughout these verses. In Isaiah 29 the imagery tries to indicate the clay does not have recourse to question the intelligence of the potter. In Romans, Calvinists try to use a similar idea to claim that God chooses some for eternal salvation and some for eternal damnation, and people have no choice and cannot complain (contrast this to Abimelech).

But this is the wrong understanding of the imagery. Although the clay is subservient to the potter, the clay is not arbitrarily molded. The reference in Jeremiah gives the Bible reader the clearest picture of what is being communicated:

Jer 18:1 The word which came to Jeremiah from the LORD, saying:
Jer 18:2 “Arise and go down to the potter’s house, and there I will cause you to hear My words.”
Jer 18:3 Then I went down to the potter’s house, and there he was, making something at the wheel.
Jer 18:4 And the vessel that he made of clay was marred in the hand of the potter; so he made it again into another vessel, as it seemed good to the potter to make.
Jer 18:5 Then the word of the LORD came to me, saying:
Jer 18:6 “O house of Israel, can I not do with you as this potter?” says the LORD. “Look, as the clay is in the potter’s hand, so are you in My hand, O house of Israel!

In verse 6, God explains that he is the potter and Israel is the clay. The story starts by the potter (God) attempting to create something nice, but the clay was “marred”. In the start of this illustration, the potter (God) does not complete his original task. Something went wrong. Instead he takes the marred clay and builds and entirely different object. This object is distinct from the original object he was trying to complete.

Calvinists have a hard time with this. To a Calvinist, God controls all things. So was God thwarting himself? Does God start projects and not complete them? Why did he begin a task he would never complete? Jeremiah goes on to explain the illustration:

Jer 18:7 At what instant I shall speak concerning a nation, and concerning a kingdom, to pluck up, and to pull down, and to destroy it;
Jer 18:8 If that nation, against whom I have pronounced, turn from their evil, I will repent of the evil that I thought to do unto them.
Jer 18:9 And at what instant I shall speak concerning a nation, and concerning a kingdom, to build and to plant it;
Jer 18:10 If it do evil in my sight, that it obey not my voice, then I will repent of the good, wherewith I said I would benefit them.

The first part of the explanation is that God will literally change his actions based on the actions of the clay (Israel). He will do the entire opposite of what he “thought to do”, if the actions of a nation changes. If God pronounces judgment, he will repent if the people repent. In fact, this happens in the book of Jonah to the evil city of Nineveh:

Jon 3:9 Who can tell if God will turn and repent, and turn away from his fierce anger, that we perish not?
Jon 3:10 And God saw their works, that they turned from their evil way; and God repented of the evil, that he had said that he would do unto them; and he did it not.

God also explains that he will repent of good if a nation becomes evil. This is the precise meaning in Romans 9. Romans 9 is not about individual salvation, but about rejecting a nation!

Rom 9:30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
Rom 9:31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.

Rom 10:19 But I say, Did not Israel know? First Moses saith, I will provoke you to jealousy by them that are no people, and by a foolish nation I will anger you.

Romans is all about God rejecting a national covenant with Israel and instead moving to the Gentiles. The illustration of the potter and the clay, does not illustrate God arbitrarily choosing some for heaven and some for hell. Instead, the potter and clay imagery illustrates that God rejected Israel based on their rejection of him. God literally changed his plan and branched out to the gentiles to make the Jews “jealous”. God’s actions, although he molds the clay, are based on the state of the clay.

God might raise up Pharaoh (Exo 9:16) to destroy him. But if that Pharaoh repents and turns to God, God tells us that he would spare that nation. God responds to his creation. God blesses and curses based on the actions of individuals. That is the meaning of the potter and the clay.