The original operating system whose usage and functionality Linux, the BSDs, and other modern "unixlike" OSes resemble and have expanded upon. Invented at AT&T's Bell Labs by Dennis Richie and Ken Thompson. It fragmented into BSD (from the SysV release) at Berkley, whereupon it fragmented some more.
For a more complete history of unix-like systems, see http://vertigo.hsrl.rutgers.edu/ug/unix_history.html
Today UNIX is a standard defined by The Open Group in cooperation with the ISO and IEEE. UNIX and POSIX are defined by the same standard now, with a stricter set of requirements for systems that claim to be UNIX. BSD is not UNIX. Linux is also not UNIX, although the list of deviations is fairly small. A number of systems have managed to earn the right to call themselves UNIX without being based on the historical source code.