First, let’s be clear that the term does not refer to a scientific theory about the brain, but, for instance, refers to my ability to form the theory that you have a mind. I might look into your eyes and recognize that there is something happening there. We can "click" on a non-verbal or even subconscious level. But I can’t know your mind directly. I can speculate that you have a sense of self identity, and that you recognize that I do too. I can only theorize that you have a mind, and I hope you will take my word for it, that I have a mind too!
I quote now from Wikipedia: “Theory of mind appears to be an innate potential ability in humans, but one requiring social and other experience over many years to bring to fruition. Different people may develop more, or less, effective theories of mind. Empathy is a related concept, meaning experientially recognizing and understanding the states of mind, including beliefs, desires and particularly emotions of others, and is often characterized as the ability to `put oneself into another's shoes’.”
For an actor, creating a character that appears to have a theory of mind is one of the greatest challenges. Anyone who has developed a close relationship with an intelligent animal will be slow to dismiss the question of that creature having theory of mind, at least to the extent of it understanding that there is a "you that is you."