Mirror neurons help children learn new skills, understand empathy, and regulate their emotions. They are brain cells that fire when a child observes another person's actions or emotions. 
Learning by imitation
Children learn new skills by watching and imitating others, such as clapping or tying shoelaces. 
Mirror neurons break down observed activities into their components, making it easier to imitate them. 
Empathy and social understanding 
Mirror neurons help children understand and share the feelings of others.
For example, when a child sees a friend crying, their mirror neurons help them feel empathy and respond with comfort.
Emotional regulation 
Children learn to regulate their own emotions by observing how others manage theirs.
For example, seeing a calm parent during a stressful situation can teach a child how to handle their own stress.
Tips for helping children develop empathy 
Model helpful empathetic behavior.
Practice empathy daily.
Encourage children to extend their empathy to animals.
Listen to what your child is saying.
Sit in the moment with your child and let them express how they're feeling.

In the mid 1800s the government of Japan banned pictures of actors to ensure moral standards remained high. As a result, ukiyo-e artists sometimes replaced the famous actors with cats. This example, from 1860, is 'The Story of Otomi and Yosaburo' by Utagawa Yoshiiku.

"The Egg Collector," Dewey Bates (1851-1899).