A small Unix like operating system written by Andrew Tanenbaum for teaching operating systems design to students, and still used today at many colleges that teach Computer Science.
Minix was designed to be small, there is a version that can run from a 360k floppy disk on a 286, with full source code and the ability to be recompiled from that disk. Minix is usually found running on PC hardware, but there is a version that can run as a process in SunOS or Solaris on the SPARC architecture.
Minix was designed to be easy to modify. Andy deliberately avoided adding unecessary features to keep the source code simple, so students could understand it.
When Linus Torvalds started working on Linux, he used Minix as a base, Linux can be thought of as a descendant of minix.
There is a famous flame war between Tanenbaum and Torvalds on Usenet about the differences between Linux's monolithic kernel design and minix's microkernel design. The debate can be found in the great (and free) O'Reilly book, Open Sources.
Minix's license was recently changed to the BSD license after two years of being sat on by Prentice Hall's Lawyers. This is a Good Thing. One of the applications of Minix (besides teaching) may be super embedded systems like wristwatches and appliances where having Unix would be beneficial, but the cost of hardware capable of running a larger OS would be prohibitive.