Anything that is fake or false is counterfeit (made in imitation of the original). This echoes the idea that man was made in the image of god, a spiritual concept. In dreams we can become acutely aware of humanity as opposed to divinity.
Psychological / emotional perspective: When we become aware that something is a fake or is false in dreams it is time for us to assess our own integrity. There are flaws or misperceptions in the way we regard ourselves.
Material aspects: A counterfeit object is one that in comparison with the original is seen to have flaws. We can admire the fake for its own intrinsic beauty while accepting the flaws. Actually fashioning fake objects suggests that we are conscious that our creativity is not being best used. Projects and tasks all have flaws that can be improved upon, and dreaming of fakes and false objects give us the opportunity to iron out difficulties before they develop into problems.