What does 'const static' mean in C and C++?

It has uses in both C and C++.

As you guessed, the static part limits its scope to that compilation unit. It also provides for static initialization. const just tells the compiler to not let anybody modify it. This variable is either put in the data or bss segment depending on the architecture, and might be in memory marked read-only.

All that is how C treats these variables (or how C++ treats namespace variables). In C++, a member marked static is shared by all instances of a given class. Whether it's private or not doesn't affect the fact that one variable is shared by multiple instances. Having const on there will warn you if any code would try to modify that.

If it was strictly private, then each instance of the class would get its own version (optimizer notwithstanding).

A lot of people gave the basic answer but nobody pointed out that in C++ const defaults to static at namespace level (and some gave wrong information). See the C++98 standard section 3.5.3.

First some background:

Translation unit: A source file after the pre-processor (recursively) included all its include files.

Static linkage: A symbol is only available within its translation unit.

External linkage: A symbol is available from other translation units.

At namespace level

This includes the global namespace aka global variables.

static const int sci = 0; // sci is explicitly static
const int ci = 1;         // ci is implicitly static
extern const int eci = 2; // eci is explicitly extern
extern int ei = 3;        // ei is explicitly extern
int i = 4;                // i is implicitly extern
static int si = 5;        // si is explicitly static

At function level

static means the value is maintained between function calls.
The semantics of function static variables is similar to global variables in that they reside in the program's data-segment (and not the stack or the heap), see this question for more details about static variables' lifetime.

At class level

static means the value is shared between all instances of the class and const means it doesn't change.