The PS3's Cell platform was based on the PPC's POWER architecture, so the PS3 was a logical next step for Yellow Dog Linux. While other distributions, including the popular Ubuntu distribution, currently work on the PlayStation 3, Yellow Dog Linux was one of the first to release a working version.
Unlike Yellow Dog Linux's parent corporation's deal with Apple, there was no deal with Sony. PS3s were never sold with Yellow Dog Linux pre-installed, it must be installed using the PlayStation 3's "Other OS" option.
The "Other OS" feature was removed by the PlayStation 3's 3.21 firmware update on March 28, 2010 New PlayStation 3s won't be able to use Yellow Dog, but older ones will if they haven't been updated. Unfortunately, not updating the firmware removes the ability to access the PlayStation Network for online gaming.
See Yellow Dog's official installation support website if you want to install this free Linux distribution on your PS3.
Image Credit: Wikimedia Commons/S. Solberg J.