Personhood in legal terms denotes that a being is capable of ruling over their own destiny legally, financially, morally and ethically - defining the state of being considered a 'person' - granting the capacity for citizenship, equality and liberty. According to law, only persons or legal personality has rights, protections, privileges, responsibilities and legal liabilities - but the topic of what is considered personhood is largely up for discuss given the wide variety of different types of minds and consciousnesses which exist.
The general concept itself revolves around the idea that a person must posess continuous consciousness over time; and who is therefor capable of framing representations about the world, formulating plans and acting upon them. This performance criterion determines agenthood. Similarly complex adaptive behavior seen in animals and machines can be difficult to distinguish from persons and one of the key defining criterions as such is that the being in question must have matters of significance, that things matter to them, that they care and need on a cognitive level, not an instinctive level - distinguishing them from animals.