Hii!
A private candidate is the one, who registeres for the exam in a particular institute, may be school or an educational board, but does not attend regular classes and just appears for the exams. So, if you appear as a private candidate, you will just have to go for exams, but study on your own. You will be considered under that particular board of education you enrolled into and a student of that particular school or university.
Hope this helps.
Good luck!