It works by programmatically parsing data from T-Square so any functionality that can be done on a desktop web browser can be done by the app. The app keeps a login session using cookies just like a web browser so you can stay logged in without storing user information.
Currently the app can only view assignments, set filters to view the assignments, and add assignments to the calendar. Assignments are cached so you can view them offline and there is a tab to view all assignments at once.
More will be implemented such as assignment downloading, resource downloading, and automatic assignment adding to calendar.