Short for 'Berkely Software Distribution'. Um, if that's "Software", why do we have BerkeleyStandardDistribution?
The original free UNIX, which actually has its roots in real UNIX. A fork of UnixOs done in large part at CalBerkeley. It shares the common heritage with System V of Unix System 6 and System 7, and therefore has much shared code. See UnixHistory and http://www.levenez.com/unix/ for Unix variant history.
Licensed under what has come to be called the "BSD license" (http://www.opensource.org/licenses/bsd-license.html); the Regents of UC later removed the advertising clause that caused RichardStallman and others so much grief.
Modern flavors are FreeBsd, NetBsd, OpenBsd, and MacOsx.