I think this is where the compression in files like JPEG files creates 'patterns' on a picture due to the amount of compression, the less of these 'artifacts' the better.
Someone more experienced should be along shortly to give you a proper explanation hopefully!
Assuming you are talking about "lossy" files like JPEGS, it means that there are "flaws" in the picture caused by compression... the more compressed something is, the more "flaws" there are...
Using very high quality settings and even after a couple saves, you shouldn't see any artifacting like that in a JPEG photo. But yes, that's what (jpeg) artifacting is.