A group in a biological taxonomy is monophyletic 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.
For example, all organisms in the genus Homo are known 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 H. habilis had developed from a different ancestor than H. 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.
See also: Linnaean taxonomy