On Earth, we use taxonomy to organize biological organisms into an identifiable hierarchy in which organisms that are evolutionarily related are placed in close proximity. This evolutionary approach to classification is a fairly recent innovation, dating back to Charles Darwin's publication of "Origin of Species."
As we Earthlings begin to move away from our little life-bearing planet, we will no doubt begin to discover organisms, living or dead, on foreign worlds (the odds are in our favor that life exists/existed somewhere other than Earth). Humans, being human, like order and like things to be neatly sorted. These new organisms would almost certainly go through the taxonomic system to be placed somewhere in the Hierarchy of Life (copyright pending), but here we face a complication.
Extraterrestrial life is highly unlikely to have evolved in the same manner as Earth life, and with even less likelihood of having a common ancestor. Our current taxonomic system utilizes evolution as a key factor in classification, but we can't know the evolution of extraterrestrial life without spending years doing field and lab work to determine how organisms are related, and short-lived, fast-paced humans want answers now.
Enter xenotaxonomy: the science of categorizing extraterrestrial life. On a given world, evolution may have evolved creatures unlike anything on Earth, or maybe creatures like we see in our myths, but not in real life: dragons, giant sea serpents, griffons, etc.
What would an effective xenotaxanomic system look like, given the desire both to have answers quickly and for the resulting hierarchy to be clear and stable?