How do scientists figure out relationships between living things?
Some scientists compare every single feature of every single organism to try to work out their evolutionary relationships. But, another group of scientists has come up with a more efficient, more reliable approach. With this method, called cladistic analysis, you only compare a few carefully selected traits.
For example, how would a scientist figure out evolutionary relationships between sharks, dolphins and wolves? Two fishy-looking animals and a four-legged, furry one.
First we need to find the ancestral line they all came from. For this, we can go to the fossil record. Fish appear in the fossil record before four-legged animals (tetrapods), so the ancestor of this group must be at least as primitive as a fish. The most ancient fish were jawless, and since our whole group has jaws, we can safely choose a jawless fish as a fairly recent ancestor.
Unfortunately, this ancestor is long dead. To compare anything besides bones, we need a living animal for comparison. For this, scientists use something called an "outgroup", a living descendant that still shares many of the ancestor's primitive traits. So we need a living jawless fish, like a lamprey.
Lampreys are jawless fishes that look a lot like sucker-mouthed eels. While lampreys have retained many primitive ancestral traits (like jawlessness and a simple fish-style body), the other descendants of our jawless ancestor branched off more recently, as they evolved new traits. But which traits do we want to compare?
Organisms have only two types of traits: primitive and derived. Primitive traits are those inherited from distant ancestors. Derived traits are those that just appeared (by mutation) in the most recent ancestor -- the one that gave rise to a newly formed branch. Of course, what's primitive or derived is relative to what branch an organism is on.
Now let's compare traits on the lamprey-dolphin-shark-wolf branch.
Dolphins and sharks both have a torpedo-like shape, so are they the closest relatives? Because the lamprey also has this shape, we know this body plan is a primitive trait and we have to ignore it.
Limbs (like those of the wolf) are a derived trait, since lampreys do not have them. If we look inside the front fins of dolphins and sharks, we find--surprise!--that the bones inside the dolphin's front flippers look a lot like wolf leg bones. Dolphins and wolves share this derived trait (and many others), so they are actually out on the same branch together. If we had been fooled by the primitive trait, we would have gotten the relationships all wrong. But why does this matter?