It's amazing to think that all the world's diverse organisms share a common ancestor, but it's true. If we could retrace our evolutionary history back to the very beginning, before there were mammals, plants, or multicellular organisms, there was LUCA, the last universal common ancestor. There may be 20 million species currently alive today, but we all arose from one LUCA.
In trying to classify and organize the world's biodiversity in an understandable way, we turn to evolution to provide us with a framework. Modern taxonomy classifies organisms based on their shared ancestry. The graphical result is a phylogentic tree that shows the relationships among organisms and the nested-ness of groups. Species are nested in genera, nested into families, grouped into orders, and so on. The diversity of the world can be traced back to the ancestors that gave rise to it.
Reconstructing a phylogenetic tree is really reconstructing the history of speciation. We often know very little about the evolutionary changes that occur within lineages, and often even less about extinctions, so speciation events become the major feature of phylogenetic trees. While speciation events lead to novel species and species traits, ancestral features are often preserved and passed on such that biologists can infer information about evolutionary relationships from shared features. Through a long history of ancestors and descendants, we are all related on the family Tree of Life.