The impact that both these art genres have on the art world is that they are pulling the focus away from the art object and toward the idea behind the art. In the Minimalist art movement, the art object was stripped down to the ‘bare bones,’ and in the Conceptualist movement, the art object is not even what the piece is about. The piece is about the idea. The object is only there to get the viewer to the idea. The roll of artist as the maker of objects is being challenged in these movements.
Take the example of Joseph Kosuth's work entitled One and Three Chairs. In the words of the The eNotes/Wikipedia page on the subject,
the piece consists of a chair, a photograph of this chair, and an enlarged dictionary definition of the word "chair"
The piece is about the different ways we have of coming to an understanding of what a thing is. We can see the thing itself; we can see a photographic representation of the thing; or we can read someone’s written account of what the thing is. Which gives us the best understanding of what a chair really is? What if the object was something we had never seen before? Would that change our ideas about which representation is the most informative or the ‘most true’. Plato would say that the ‘most true’ chair is the idea we have of the quintessential chair. The one that we have in our head, and the one to which we compare all the chairs we ever see, before we come to the conclusion that what we are looking at is indeed a chair.
Is this all really interesting to think about?... Yes. But, is it a beautiful piece to look at?… No. Did Joseph Kosuth actually make the chair in his piece?… No. OK, so he did photograph it and he did blow up the definition with a large printer, but I think you will agree that this piece is not about the art object.
Let’s look at the minimalist work of Donald Judd or Tony Smith both of whom make large sculptures that appear to be a series of perfect industrial looking boxes. Some of the boxes have a metallic sheen; some are pure black; some are arranged to create an altered rectangular form; and some are bolted to a wall one on top of the other with small spaces in between. These artists are trying to call your attention to the beauty of the pure rectangular form. When you think about it, these pieces are real monuments to human creation. They are representations of the simplest thing that cannot be made by nature alone. But, are they beautiful to look at?… No. Did Donald Judd and David Smith actually make any of these grand box forms themselves?… No. They designed it, planned it, and then sent the plans to an industrial fabrication company that made them out of the decided material.
So, to sum up, Minimalist art and Conceptual art is really fun to learn about, and talk about, and write about; but for many people it is difficult to enjoy visually. The reason is that this type of work is not about creating a beautiful art object. These movements represent how the art world is moving away from artists in the role of craftspeople and towards artists in the role of philosophers.