Mirror neurons and differences in imitation patterns of humans and other primates.
Mirror neurons, studied extensively in Rhesus monkeys using single-cell recording techniques, have been used to explain a number of phenomena in humans: imitation, empathy, theory of mind, and language acquisition (to name just a few.) However, the mirror system in humans has only been indirectly studied using imaging techniques, leaving much room for speculation as to what exactly the human mirror system does and if it is at all similar to the mirror neurons found in our distant relatives, Macaca mulatta.

Rhesus monkey.
So what does a mirror neuron do, anyway? The mirror neurons studied in Rhesus monkeys do two things: they fire when the monkey reaches for an object, and they fire when the monkey watches someone else, such as a human experimenter, reach for an object. For this reason, it has been claimed that mirror neurons form the basis of imitation, allowing the individual to map someone else’s actions onto their own actions. If I see you stick out your tongue, I can stick out my tongue too. I can imitate you, all thanks to my mirror neurons.

Newborn human infants are capable of imitation.
There’s just one problem: chimps, our closest primate relatives, don’t imitate, at least not the way humans do. Human infants and children will imitate all kinds of actions by adults. For example, newborn human infants will stick out their tongue in response to someone else sticking out theirs. While watching an adult perform a series of actions, some relevant and some irrelevant, in order to solve a puzzle, human children will repeat all of the actions in the sequence, even if they are irrelevant to the task. Chimps, on the other hand, will imitate only those actions that are relevant to solving the problem, ignoring the irrelevant actions.

Chimps only imitate actions that are important to solving a task, such as retrieving the contents of the puzzle box pictured above. Human children, on the other hand, will imitate every action, including those that are irrelevant to the task.
Some researchers have suggested that in chimps, the mirror system is not for imitating low-level kinematic features of action, as a baby does when they stick out their tongue after watching someone else do the same. Rather, the mirror system in chimps might serve the purpose of extracting the goal structure of the observed action - that is, for understanding that an agent is performing a goal-directed action for a purpose, such as when someone reaches for an object. The mirror system might aid the chimp in representing the intentional actions of agents, as it is active when perceiving a goal-directed movement, including one’s own, which is indeed what happens when the rhesus monkey itself reaches for an object.
This leaves open two possibilities: the mirror system in humans might be qualitatively different than the mirror system in other primates, representing only low-level kinematic features rather than the goal structure of an event, or the human mirror system is more refined than that of other primates, allowing humans to encode intentions more flexibly, resulting in the different patterns of imitation found in humans and other primates.
Ref: Lyons, D. E., Santos, L.R. & Keil, F.C. (2006). Reflections of other minds: how primate social cognition can inform the function of mirror neurons. Current Opinion in Neurobiology, 16(2), 230-239. View