Reports.php - This file is exclusively for generating reports to help assist forum administrators keep track of their forum configuration and state. The core report generation is done in two areas. Firstly, a report "generator" will fill context with relevant data. Secondly, the choice of sub-template will determine how this data is shown to the user.
Register.php - This file has two main jobs, but they really are one. It registers new members, and it helps the administrator moderate member registrations. Similarly, it handles account activation as well.
Recent.php - This file had one very clear purpose. It is here expressly to find and retrieve information about recently posted topics, messages, and the like.