2. An aid to prediction: If one knows that all members of a particular group have a certain set of characteristics, then there's a good bet that a new member of that group may also have some of those (useful?) characteristics, too. (such as antibiotic production, edibility, etc.)
3. An aid to explaining evolutionary relationships
4. Provides a stable, relatively unchanging system of internationally recognizable names.

You can learn much more about how to read phylogenetic trees at the UC Berkeley Museum of Paleontology.
Another fantastic resource showing a variety of very up-to-date phylogenetic trees can be found at the Tree of Life Web Project.
In the earliest studies of biodiversity
In 1735, Swedish botanist Carl Linne (a.k.a. Linnaeus) published Systema naturae,outlining a new system of binomial nomenclature. It's still in use today.
In the Linnaean system, every scientific name consists of an organism's Genus and species, the names of which are always GREEK, LATIN or LATINIZED versions of other languages or terms.
Example:

Each species is nested in every taxonomic level above genus in ever more inclusive groups:
DOMAIN - Kingdom - Phylum - Class - Order - Family - Genus (plural =
genera) - species
(Insert clever mnemonic device here)
For the rabbit, this would break down as...
In general, scientific names have a specific meaning, usually describing the species. For example, Eleutherodactylus planirostris, the Greenhouse Frog:

Many species are at least partially named after people, but these proper names, too, must be Latinized:

A Taxon Has Three Aspects:
1. Its name
2. Its rank
The relative rank of a given organism within its larger and smaller groupings is more relevant than the rank itself, which is subject to change.
For example, it's important to know that all members of Felis (cats) are classified within the larger taxon "Carnivora," (carnivores) and that all carnivores are classified within the still larger taxon "Mammalia" (mammals).
It's less important to know that "Carnivora" is an order and "Mammalia," is a class (especially since those ranks can change with new data).
(In fact, many institutions now use rankless system in publication, in which taxa are described only by their name, with rank being tacitly understood. An author using this system will write "Mammalia" rather than "Class Mammalia" to avoid confusion as the ranks shift and change along with new information.)
3. Its content
2. No two species or genera may have the same scientific name.
3. The name must be Latin or Latinized
Example: The bones in the forelegs of various vertebrates.

An analogous structure found in two different species
Example: The wing of a butterfly and the wing of a bat.

How do we know the common ancestor of the butterfly and the bat didn't pass on the wings to both species? You'll have to trust me on this, but if you follow the embryo development of a butterfly and a bat, you'll see that their most recent common ancestor probably looked something like this:

(A little, microscopic thing called a gastrula.)
No eyes. No head. No wings.
The wings of the butterfly and the wings of the bat evolved independently, long after their ancestral lineages diverged.
Example: All vertebrates have a bony tail posterior to the anus.

It was present in the ancestral vertebrate, and though different vertebrates have evolved differently shaped tails, they are all evolved from the common ancestral tail. The PRESENCE of the tail is primitive.
Example: the modified shapes of various vertebrate tails. An extreme example: The loss of the external tail in great apes (including humans). The baboon shows the primitive condition, whereas the gorilla and Very Handsome Man show the derived condition of the post-anal tail.

(We still have a tail; it's just very reduced and tucked where it doesn't show.)
Note that these are comparative terms. You can't say something is "primitive" or "derived" without comparing it to something else. In systematics, you'll be comparing two related species, perhaps an ancestor and its descendant, or perhaps two related species.
Systematists use the existence of shared characters to help reveal their common ancestry.
Here's how this works, using our own family (Pongidae; Great Apes) and our own species (Homo sapiens) as an example.
Here are the hypothetical evolutionary relationships of apes.
This phylogenetic tree (from Human Molecular Genetics - Evans, 2004) is based upon amino acid sequences in a protein called ASPM, which is believed by some to be involved in the formation of the central nervous system (brain and spinal cord) in vertebrates.
You'll notice that there's an animal on there who's not an ape: The Owl Monkey.
We use this species because we know it has more primitive characteristics than the Great Apes we're studying, so we use it as an outgroup to find out which Great Apes are the most primitive. If some great apes share primitive characters with Owl Monkeys, but others have the same characters in highly derived form, we usually can say that the ones more similar to the Owl Monkeys are more closely related to Owl Monkeys, so they branch off first.
The more symplesiomorphies a taxon within your study group shares with the outgroup, the more likely it is that it shares a more recent common ancestor with that outgroup. This means it may be more primitive than other members of the group you're studying.
Only synapomorphies help us establish recency of common descent among related organisms.
The more synapomorphies two groups exhibit, the more recent their common ancestor. Let's see how this works by using our TAILS again.
A taxon's evolutionary history/relationships can be diagrammed with a phylogenetic tree such as the one above. Each branch point represents a hypothetical ancestor of all the taxa above it on the tree.
Thus, you cannot correctly say that any species evolved from another species. You can say only that two species share a common ancestor.
Let's try this together. True or false:
What do you think?