Another one of Computer Sciences invented words. Seldom heard outside of technology circles, though many EEs will use it in reference to non-tech objects, much to the chagrin of anyone in earshot.
The concept is simple in that, if something is standalone, it stands alone; this has different variations from thing to thing.. In the case of computers themselves, standalone is usually used in deference to the machine being networked or not. In software, it applies to programs that can run on their own two feet, versus code or programs that rely on other code or programs being present in order to function.