You've certainly asked a question which is difficult to answer with any definition, and a detailed explanation would probably take a life's work written across several volumes, plus years of introspection to get anywhere close. But then, that's why you asked it, didn't you? So lets have a brief think about this.
A person is a centre of awareness of him or herself manifesting through the senses and super-senses inherent in their physical and mental bodies. They are the observer, the witness, the experiencer of their lives. They are aware of the 'I am,' i.e. I am me, if you were to put it into words.
They are not the body, or the thoughts. These are the tools of mind. But these tools appear, at times, to have wills of their own and quite often the 'I am' identifies with the thought and there, albeit temporarily, it is - in the Biblical term - 'cut off from the vine.'
The Human Person is the spark of life within. It is the everlasting part of all of us. The spark is within all things, animate and inanimate, I suspect. But in human beings it is aware at the deepest levels of its being that it IS this spark. At the more conscious, superficial level, of course, it asks questions such as:
What is a Human Person? so it can link up with more of itself through others. For it is a part of The Whole...and we all desire to be more of The Whole.