A Multitasking, multiuser Unix kernel, usually combined with GNU software to make a GNU/Linux system.
The AmigaOne and Pegasos both run GNU/Linux, and Classic Amigas can run 68k GNU/Linux. At one point, Gateway was considering using GNU/Linux as the basis for a new AmigaOS.
It's not easy for an average user to make a system out of the bare Linux Kernel and add software, so most people buy distros. A good CD based Debian flavored GNU/Linux demo for x86 PCs is Knoppix (http://www.knopper.net/knoppix/index-en.html).
AROS is able to run within a Linux task, creating a system very similar in concept to the MorphOS ABox idea.