Internal Nodes are the connection points on a phylogeny. They represent some common ancestor between two tips or two groups of tips. For example, on this example phylogeny for apes, we see that humans and chimpanzees are joined by the internal node highlighted in Red.
Thus, this internal node represents some common ancestor between chimpanzees and humans (as well as Bonobos!). Nodes provide the inherent structure of phylogenies and are critically important to understanding the relationships between taxa.