What does “static enum” mean in C++?

That exact code, with just the ellipsis removed, is not valid C++. You can’t use the static storage class specifier in an enum declaration; it doesn’t make any sense there (only objects, functions, and anonymous unions can be declared static).

You can, however, declare an enum and a variable all in one declaration:

static enum Response {
    NO_ERROR = 0,
    MISSING_DESCRIPTOR
} x; 

The static here applies to x and it is effectively the same as if you said:

enum Response { 
    NO_ERROR = 0,
    MISSING_DESCRIPTOR
};

static Response x;