Is XBMC for the Raspberry Pi an operating system?
Or is it built on top of another, such as Debian?
XBMC is not an operating system, but a cross-platform media player. It needs an existing operating system in order to be installed and run.
From the XBMC website:
XBMC is an award-winning free and open source (GPL) software media player and entertainment hub for digital media. XBMC is available for Linux, OSX, and Windows. Created in 2003 by a group of like minded programmers, XBMC is a non-profit project run and developed by volunteers located around the world. More than 50 software developers have contributed to XBMC, and 100-plus translators have worked to expand its reach, making it available in more than 30 languages.
Just a little addition to IRO-bot's answer, someone has bundled XMBC together as image for the Raspberry Pi: http://www.raspbmc.com/about/