Mirror neurons are special neurons in the brain that underlie the experience of empathy and also play a critical function in learning. What makes them distinct is that they fire both when performing a certain action and observing another person, especially of the same species, perform that action. So the neuroactivity is the same whether it's the individual performing the action or someone else. Two locations in the brain where these neurons have been observed are the premotor cortex and the inferior parietal cortex. The are likely a common neurological feature of many if not all primates.
The phenomenon of mirror neurons proves that seeing really is believing. They underscore the reality that perception is not a one-way conduit from reality to the brain, but rather a complex feedback cycle between the two. When a person sees someone who he thinks is in pain, he can feel a weaker form of that pain. If that person sees someone performing a complex motor action, he can imagine himself performing that action. Mirror neurons are probably a big part of what lets apprentices pick up skills from their masters.
These neurons were originally discovered in macaque monkeys in the 1980s by Italian neuroscientists Giacomo Rizzolatti, Leonardo Fogassi, and Vittorio Gallese. Since their discovery, they have been hailed as one of the most significant recent findings of neuroscience and have been implicated in everything from sensorimotor learning to language learning to folk psychology theories. A deficiency has been theorized as the underlying neurological reason for the pathology of autism, or "mind-blindness."
The discovery of mirror neurons is intuitively interesting to many people because they have experienced their effects first-hand. These neurons are probably a big part of why emotions, such as rage or pleasure, can be contagious, and they would seem to underlie mob psychology. Depending on how vivid a portrayal of someone experiencing a given emotion or performing a particular task is, the more neurons are activated and the more visceral the experience is. This is why movies tend to hit home harder than photographs, which in turn seem more emotionally tangible than text.
Even text activates some category of mirror neurons because most people "hear" text in a voice as they read it. This disembodied voice creates a subtle illusion of the presence of another person undergoing a thought process, and people can empathize with various facets of it on that basis.