A monophyletic group consists of organisms that share recent common ancestors and therefore have similar features.
Another way of thinking about monophyly is to ask whether or not ALL of the members of a previously classified group (a genus of plants, for example, that may have been described by Linnaeus) are all descended from a single "most recent common ancestor" that ONLY gave rise to species classified in that named group. A monophyletic taxon does not include species that really belong to another evolutionary lineage, and should include all of the relevant members of the evolutionary group. Put another way, this is a way of ensuring that our classification schemes correspond as closely as possible to evolutionary lines of descent. So, monophyletic classifications are where linnaean taxonomy (18th century) meets Charles Darwin (19th century), using 21st century science! As an example, think of the monocot family Liliaceae. Recent classifications of this family (based on various lines of morphological and molecular evidence) now exclude many petaloid monocots (such as onions, daffodils and Alstroemeria) that were placed there in outdated classifications, but that we now know to belong to completely different families or orders of monocots. Our new classification of Liliaceae is monophyletic, but the old schemes were not!
