Bibliotics is the scientific study of handwriting. Often, the purpose of bibliotics is to determine who wrote something.
Words with the root biblio always involve books or writing. In this case, bibliotics is the study of how people write: specifically, their handwriting. An expert in bibliotics will analyze examples of handwriting from a scientific point of view. This could have several purposes. For old documents, you might want to know if a famous person really wrote something. In law enforcement, bibliotics could be used to determine who wrote a ransom note or another piece of written evidence.