For example, all organisms in the genus Homo are believed to have come from the same ancestral form in the family Hominidae, and no other descendants are known. Thus the genus Homo is monophyletic. If, on the other hand, it were discovered that Homo habilis had developed from a different ancestor than Homo sapiens, and this ancestor was not included in the genus, then the genus would be polyphyletic. Since biologists by and large prefer groups to be monophyletic, in this case they would likely either split the genus or broaden it to include the additional forms.
It should be noted that sometimes the term holophyletic is used for the sort of groups discussed here, and monophyletic is used to mean holophyletic or paraphyletic.