IRIX is Silicon Graphics' (SGI) proprietary Unix-like operating system for its systems. It was originally BSD-based up to version 6 when it became a System V rewrite. Released with SGI's first system in 1982, it originally did not have an actual name until late 1986 when the 4D based Personal IRIS systems became avaliable. At that point up until 1992, the operating system was known as 4D1 and lasted from branches, 3.x to 4.x. With the arrival of the 5.x branch, the name became IRIX (Although for quite some time prior, uname would produce IRIX), after the original SGI systems, the IRISes.
Originally, IRIX used Sun Microsystems' NeWS Postscript-based window manager until the X Window System became the official standard. IRIX also comes with a wide assortment of demos to show off your system's awesome 3D graphics abilities. It also has a very well developed set of GUI system administration tools that make the operating system very user friendly. Continuing with X Windows, IRIX has its own window manger, 4Dwm (It can run others, like Enlightenment.). It is a very simplistic window manager with lots of SGI extensions. Recently, a clone of 4Dwm has been made for Linux called 5Dwm. Visit http://www.5dwm.org/ for more information.
SGI designed IRIX for both its high-end workstations and supercomputers, IRIX has extremely good scalability and can address massive amounts of memory. It moved from a 32-bit operating system, to a 32-bit, 64-bit hybrid around 1993 and eventually became a 64-bit system around 1997 although it still supports 32-bit processor mode for certain older systems that require it (You can see if you have a 32-bit or 64-bit IRIX system by doing uname. IRIX64 means a 64-bit system, and IRIX is just a 32-bit one.). The backwards compatability of IRIX also extends to software, it can run IRIX programs more than 10 years old (IRIX 6.2)!
IRIX is not without its flaws. A fresh installation of IRIX is not as bad as one thinks it is, although completely text based, it's fairly automated. One of the only major gripe is when certain software distributions conflict and you have conflicts 1, 2, 3, 4...etc, and options A, B, and C for each. You would then have to type for every single one, > conflicts 1a 2a 3c 4c...and so on. As a result, it is suggested that you use default as the install mode and go install your software after the system has installed and can be used. Another other major irritation is locking down the system. IRIX assumes that it's installed behind a secure network, so, have fun. Last, IRIX is full of security holes, this is kind of a trade off since some of the security holes are intertwined with the "coolness" of an IRIX system.