In C, what does a variable declaration with two asterisks (**) mean?

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It declares a pointer to a char pointer.

The usage of such a pointer would be to do such things like:

void setCharPointerToX(char ** character) {
   *character = "x"; //using the dereference operator (*) to get the value that character points to (in this case a char pointer
}
char *y;
setCharPointerToX(&y); //using the address-of (&) operator here
printf("%s", y); //x

Here’s another example:

char *original = "awesomeness";
char **pointer_to_original = &original;
(*pointer_to_original) = "is awesome";
printf("%s", original); //is awesome

Use of ** with arrays:

char** array = malloc(sizeof(*array) * 2); //2 elements

(*array) = "Hey"; //equivalent to array[0]
*(array + 1) = "There";  //array[1]

printf("%s", array[1]); //outputs There

The [] operator on arrays does essentially pointer arithmetic on the front pointer, so, the way array[1] would be evaluated is as follows:

array[1] == *(array + 1);

This is one of the reasons why array indices start from 0, because:

array[0] == *(array + 0) == *(array);

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