Definition - What does Unix Box mean?
A Unix box is a computer, typically a desktop or server, that runs any of the several flavors of Unix-like operating systems (OSs) such as Linux, Solaris or Mac OS X. The term came about in order to distinguish computers running Unix-like OSs from the more common Windows PCs when talking about them online in forums or in person.
Techopedia explains Unix Box
Unix box is a term used mainly by IT professionals and administrators to refer to computers running Unix-like OSs. This typically refers to servers running a Unix-like OS since, when talking in forums, especially for administrators, there is a need for a quick way to differentiate the different servers and the easiest seems to be naming the OS instead of the model of the server. Therefore, instead of saying "I need help with security administration in my Dell XX server," which could get confused with the same models running Windows Server or other types of OS, they can simply say "I need help with the security administration of my Unix box". It avoids confusion, and since Unix-like OSs share many of the same functionalities, the discussion could go right into the details instead of inquiring about the unit and the OS it runs.