The point was that the coin, bearing Caesar's image, ostensibly belongs to Caesar ultimately...And that likewise, we ourselves, bearing the image of God (Gen 1:26, "Let Us make man in Our image"), belong to God and should give our lives fully to him.
Discussion
I get the second part about our lives belonging to God; it's the first part about what is Caesar's that has always troubled me.
So in the US, our money bears Washington's image; so then our money belongs to Washington? Or, if the government has issued your money then it actually belongs to them? That, in itself, is an argument for using Bitcoin or other non-government issued money.