The cells were discovered in monkeys and they fire when observing the behaviour of others. Apart from that, their precise role is not known. Some researchers claim that defects in the system are implicated in autism.
Mo Costandi writes in The Guardian :
Mirror neurons have proven to be highly controversial. A handful of brain- scanning studies show that several regions of the brain are activated during both action execution and observation, and it has been suggested that these areas constitute the human mirror system. But while hundreds of other studies attempt to explain their results by alluding to mirror neurons, very few actually provide hard evidence.
So there is, as yet, very little convincing direct evidence that mirror neurons exist in the human brain. In fact, a number of studies have failed to find evidence of human mirror neurons altogether.
While we might expect humans to have similar nervous systems to monkeys, it may be that humans use different equipment for monitoring and responding to the behaviour of others.
Hat tip: Stephanie West Allen at Brains on Purpose