What does "const class" mean?

The const is meaningless in that example, and your compiler should give you an error, but if you use it to declare variables of that class between the closing } and the ;, then that defines those instances as const, e.g.:

const class A
{
public:
    int x, y;
}  anInstance = {3, 4};

// The above is equivalent to:
const A anInstance = {3, 4};

What does "const class" mean? It seems to compile ok.

Not for me it doesn't. I think your compiler's just being polite and ignoring it.

Edit: Yep, VC++ silently ignores the const, GCC complains.

If you had this:

const class A
{
} a;

Then it would clearly mean that 'a' is const. Otherwise, I think that it is likely invalid c++.

Try compiling it with GCC, it will give you below error:
error: qualifiers can only be specified for objects and functions.

As you can see from the error that only objects(variables, pointers, class objects etc.) and functions can be constant. So try making the object as constant, then it should compile fine.
const class A {};
const A a ;