Every church always needs new members. Traditionally, churches have invited the public in to see holiday events or have reached out to the community by doing charity work, all with the hope of attracting more people. In Russia, the Russian Orthodox church had the same problem, so they decided to promote their church through a calendar.
While most church calendars might display holy icons of some kind, the Russian Orthodox church decided to use pictures of priests with their cats instead. The idea is that since cats are so popular on the Internet, they should be equally popular on calendars.