Monophyly means common descent from a single ancestor. Biologists have introduced a kind of taxonomy called cladistics. The aim of this is to make biological classification fit what we know about the way organisms evolved.
A group which contains organisms, without their common ancestor, is called polyphyletic. If a group contains the common ancestor, but leaves out some of its descendants, it is called paraphyletic. All living things on this planet are thought, on the basis of DNA analysis, to be monophyletic, that is, to have one origin, not many.
If, on the other hand, it were discovered that Homo habilis had developed from a different ancestor from Homo sapiens, and this ancestor were not included in the genus, then the genus would be polyphyletic. Since biologists by and large tend to prefer monophyletic groups, in this case, they would likely either split the genus or broaden it to include the additional forms.
Example of polyphyletic group: Sea slugs.
Sometimes taxonomists are frustrated fitting plant species into a monophyletic group because of polyploidy. There is clear evidence that some polyploid plant species are of multiple origins (the species has arisen more than once). For example Salsify, the hybrid goat's-beard, (Tragopogon miscellus) has formed as many as 20 times in eastern Washington.
Also, it can happen that hybrids between two close plant species undergo polyploidy, and the polyploids continue as a new and distinct species. Situations like this are outside the normal rules of descent, and are dealt with by special decisions, guided by the International Commission of Botanical Nomenclature (ICBN).
Images for kids
Phylogenetic tree, the blue (left) and red (right) groups represent monophyletic groups, the green group (centre) being paraphyletic.
Monophyly Facts for Kids. Kiddle Encyclopedia.