Mirror neurons have been discovered by Italian scientists (Rizzolatti, Gallese) in 1996 while they were conducting experiments on primates.
While the primates were observing the scientists picking up stuff, researchers measured brain activity in the same area where it would be if the primates were actually performing the actions themselves. Furthermore, the activity was situated in the inferior premotor cortex, while everyone believed the processing of external stimuli could only take place in the other half of the brain. Appearantly, these neurons helps primates to understand each other.
Needless to say, scientists wanted to discover this 'mirroring' in human brains. And indeed, this behaviour (a bit more complex, though) was found in Broca's Area.
Luckily, simular to our primate friend's brain, our brain suppresses the impulses generated by mirror neurons, otherwise we would constantly imitate eachother. Experiences with demented people prove this theory.
Scientists believe mirror neurons play an important role in our communications skills, particulary in languages.
Some say a malfunctioning mirroring system could be the cause for autism.