Showtime, now known as Movian, is a media center program ported to the PS3. It allows the playback of audio files as well as most video files, including ones not natively supported by the PS3 (mkv, mpg, etc.), even from NTFS hard drives. Plugins for Movian can be downloaded from within the app and include YouTube, Navi-X, OpenSubtitles, and various global TV stations. Files can be played from an external hard drive as well and can be organized and marked as watched.
Showtime Disk Access is a fork of Movian that allows you to utilize Blu-Ray movies, photo disks, or music CDs in the Blu-Ray drive. You can also take screenshots of movies, play music while a photo slideshow is playing, and use Remote Play to watch videos on compatible devices.
If using the official Movian app, you must download the Play store version, update by clicking "Open Download" at the top and "Install Update", and you should be able to see your PS3's Movian server inside the Local Network tab on the main menu. Tap it, and you will be able to control it on your TV.
If using Movian Remote, tap the settings button in the top right, and then "IP Address". Enter the IP address found in the Settings column → Network Settings → Internet Connection and Status List, and you will be able to use the controls on the home screen to manipulate Movian on your PS3.
Movian has plenty more plugins due to the active development of this homebrew.