Paraphyletic taxon comprises - a group of organisms that are descendants of a common ancestor and their most recent common ancestor itself. It is similar to monophyletic group, just that, unlike a monophyletic group, all the descendants of the most recent common ancestor are not included.
All the organisms, being the progeny of this most recent common ancestor have many common features. Paraphyletic taxon is a natural group; some examples are Class Pisces, Gymnosperms, etc.
Polyphyletic taxonomic group, on the other hand, is a group in which the most recent common ancestor of the organisms in the group is not there.
Polyphyletic taxa are not much in use now because they were thought to be unnatural. Some examples are; marine mammals, order Insectivora (an abandoned taxa), etc.
Please note that using the term “most recent common ancestor” is important because all living organisms, eventually, are supposedly the descendants of one common ancestor. And so all groups will, ideally, become monophyletic.