Fedora was the underlying operating system on the OLPC XO-1, XO-1.5, XO-1.75 and XO-4 laptops. This is the Linux distribution (previously called "Fedora Core") developed by Fedora Project and sponsored by Red Hat.
Because it is the Linux base chosen by the OLPC on which to develop Sugar, it is a reference for any other Linux distribution attempting to run on the OLPC XO hardware or present the Sugar UI on a conventional computer.
Each OLPC software release had been based on a version of Fedora, for example 13.2.7 is based on Fedora 18. Over time, the OLPC operating system had moved closer to a "stock" Fedora release with some additional OLPC packages, created with the OS Builder tool.
If you have a Fedora distribution running on a computer, you can install the Sugar environment that runs on the XO laptop.