UNIX, despite its pronunciation, has nothing to do with falsettos. It is the ancestor of many operating systems, including GNU/Linux and OS X. It was first announced in 1971 by Bell Labs (then partially owned by AT&T), but was proprietary non-free software.
This prompted Richard Stallman to create the GNU (for “GNU's Not Unix!”) Project and popularize the idea of FLOSS. The GNU system was missing an important component, however- the kernel. It was then that Linus Torvald created the Linux kernel, giving rise to the GNU/Linux OS.
Since GNU/Linux is FLOSS, it does not share any actual proprietary code from UNIX. Instead, it inherited many of its attributes, including the "UNIX philosophy", which stresses writing small, simple modular programs which each do one thing very well, rather than large, complex programs which try to do many things. This is why GNU/Linux can be mixed-and-matched with many different components, including different DEs and Package Managers.