Linux is a high-profile computer operating system. The Raspberry Pi can run one of a number of Linux distributions, the most pupular being Raspbian (Debian-based) and Arch Linux.
Linux colloquially refers to open source operating system distributions based on the Linux kernel and GNU userspace fundamentals. This includes the Foundation recommended Raspbian, as well as others such as Arch Linux, and, on the Pi 2, various forms of Ubuntu, e.g. Snappy Core.