There is only one file type that uses the .THEATER extension:
iMovie Theater File
Archive created by iMovie 10 and later, a video editing application; contains files that make up a user's iMovie theater, which includes .MP4 files of the user's videos and a .PLIST file containing a list of the seen movies.
When you select the "Theater" view in iMovie, the application displays the information held in the THEATER file. The iMovie Theater is made up of movie projects that you have created and shared. The THEATER file is located in the "Movies" folder of the user directory.
Updated: October 14, 2014