Clades and Cladograms: Helpful Concepts to Understanding Phylogeny and the Hereditary Links Between Plant Groups
Cladistics is a system of classification…of course it is…that relates species to one another based on heredity and lines of inheritance. Before you dismiss this as a totally boring topic, consider that these are tools, that with a little study, can go a long way in clearing up the murky waters of taxonomy and systematic botany. Cladograms are a diagrammatic, graphic devices to visually display the relationships of closely related organisms, like the one below, and can be helpful to us in our efforts to understand the phylogeny and evolution of plants. The ‘branches’ of a Cladogram represent clades, all of the descendants are of a chosen ‘root’ species. Each clade must be monophyletic, complete, including all of the descendants of the root or ‘stem’ ancestor. The APG demands precision.

“Cladogram (family tree) of a biological group, showing the last common ancestor of the composite tree, which is the vertical line ‘trunk’ (stem) at the bottom, with all descendant branches shown above. The blue and red subgroups (at left and right) are clades, or monophyletic (complete) groups; each shows its common ancestor ‘stem’ at the bottom of the subgroup ‘branch’. The green subgroup is not a clade; it is a paraphyletic group, which is incomplete here because it excludes the blue branch even though it is also descended from the common ancestor stem at the bottom of the green branch. The green subgroup together with the blue one forms a clade again.” (emphasis mine) This is from Wikipedia, generally a good source for an overview.