A group in a biological taxonomy is monophyletic (greek: of one stem) if all organisms in that group are known to have developed from a common ancestral form, and all descendants of that form are included in the group. Taxonomic groups that contain organisms but not their common ancestor are called polyphyletic, and groups that contain some but not all descendants of a given form are called paraphyletic.
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.