What is a person? It's an important question because the way that a human behaves towards another lifeform is determined by whether the human believes the other lifeform to be a person or not.
In the introductory commentary to the Penguin Classics Deluxe Edition (2005) of the Tibetan Book of the Dead, the Dalai Lama describes the Tibetan Buddhist view of what constitutes a person, as set out below."Among the ancient schools of thought, which accepted the notion of continuity of consciousness, there were several non-Buddhist philosophical schools which regarded the entity, the 'I' or 'self', which migrated from existence to existence as being unitary and permanent. They also suggested that this 'self' was autonomous in its relationship to the psycho-physical components that constitute a person. In other words they believed or posited that there is an essence or 'soul' of the person, which exists independently from the body and mind of the person.
"However, Buddhist philosophy does not accept the existence of such an independent, autonomous entity. In the Buddhist view, the self or the person is understood in terms of a dynamic interdependent relationship of both mental and physical attributes, that is to say the psycho-physical components which constitute a person. In other words our sense of self can, upon examination, be seen as a complex flow of mental and physical events, clustered in clearly identifiable patterns, including our physical features, instincts, emotions, and attitudes, etc., continuing through time.
"Further ... this sense of self is simply a mental construct, a mere label given to this cluster of dependently arising mental and physical events in dependence on their continuity.
"Now, when we look at this interdependence of mental and physical constituents from the perspective of Highest Yoga Tantra, there are two concepts of a person. One is the temporary person or self, that is as we exist at the moment, and this is labelled on the basis of our coarse or gross physical body and conditioned mind, and, at the same time, there is a subtle person or self which is designated in dependence on the subtle body and subtle mind. This subtle body and subtle mind are seen as a single entity that has two facets. The aspect which has the quality of awareness, which can reflect and has the power of cognition, is the subtle mind. Simultaneously , there is its energy, the force that activates the mind towards its objects --- this is the subtle body or subtle mind. These two inextricably conjoined qualities are regarded, in Highest Yoga Tantra, as the ultimate nature of a person and are identifies as buddha nature, the essential or actual nature of mind."
The above is the Tibetan Buddhist perspective on personhood. There are other perspectives, depending on where one stands! The "personhood" issue has been extensively analysed in this blog.