A monophyletic group is a group that contains a common ancestor and all of its descendants. If we look at this phylogeny of the vertebrates we can create many different monophyletic groups.
If we start at any node and find all of its descendants, we can create a monophyletic group. Monophyletic groups are a useful tool for helping us understand our phylogenetic tree and for naming similar groups on the tree of life! For example, on the below phylogeny we created a monophyletic group which includes the primates and the rodents. This group on this phylogeny, represents the mammals!
The field of systematics relies heavily on monophyletic groups to define taxonomic ranks such as species, genus, or family.
You may also hear monophyletic groups referred to as a clade. A single tip can be considered a clade, however, it is most often used to describe a group of tips.