As the name suggests, its primary purpose was the state security, i.e., struggle against hostile organizations: plots, terrorists ("bombists"), socialists, and revolutionaties.
The task was performed by all means, including covert operations, undercover agents, "perlustration" -- reading of private correspondence. Even its Foreign Agency served this purpose. The Okhranka is notoriously known of its agents provocateurss Azef, Bogrov, the Bloody Sunday event, and fabrication of the antisemitic Beilis trial.
Charles A. Ruud, Sergei A. Stepanov; Fontanka 16 - The Tsars' Secret Police; McGill-Queen's University Press (paperback, 2002) ISBN 0773524843