If you accuse someone of pedantry, you mean that you disapprove of them because they pay excessive attention to unimportant details or traditional rules, especially in connection with academic subjects.

A pedant is a person who is a formalist or precisionist in teaching or scholarship. The term comes from the Latin word paedagogare, meaning "to teach", derived from Greek terms for "child" and "to lead." The term is typically used in a negative connotation, indicating someone overly concerned with minutiae and detail.

Pedantry can also be an indication of certain developmental disorders. In particular those with Asperger Syndrome, or Higher Functioning Autism, often have behavior characterized by pedantic speech. Those with Asperger's tend to obsess over the minutiae of subjects, and are prone to giving long detailed expositions, and the related corrections, and may gravitate to careers in academia or science where such obsessive attention to detail is often rewarded.

More Info: psychology.wikia.org