The simple interface consists of the big left part of the button and can be used to instantly show all Featured pictures, Quality images, or Valued images in and below the current category.
A gallery of images with positive assessments in Category:Idaho, note the strength-of-match slider to refine the results in real time and the opened menu with advanced operations.
The advanced interface is accessible through the dropdown menu activated by the right part of the button. Through this menu operations like arbitrary category intersections can be performed.
The backend server is running on Wikimedia Labs project (and could be scaled by adding more instances). Response times on typical categories are in the sub-second range. Longer running queries stream status updates (via WebSockets, if available) and display progress to the user.