What is a nested name specifier?

::S is a qualified-id.

In the qualified-id ::S::f, S:: is a nested-name-specifier.

In informal terms¹, a nested-name-specifier is the part of the id that

• begins either at the very beginning of a qualified-id or after the initial scope resolution operator (::) if one appears at the very beginning of the id and
• ends with the last scope resolution operator in the qualified-id.

Very informally¹, an id is either a qualified-id or an unqualified-id. If the id is a qualified-id, it is actually composed of two parts: a nested-name specifier followed by an unqualified-id.

Given:

struct  A {
    struct B {
        void F();
    };
};

• A is an unqualified-id.
• ::A is a qualified-id but has no nested-name-specifier.
• A::B is a qualified-id and A:: is a nested-name-specifier.
• ::A::B is a qualified-id and A:: is a nested-name-specifier.
• A::B::F is a qualified-id and both B:: and A::B:: are nested-name-specifiers.
• ::A::B::F is a qualified-id and both B:: and A::B:: are nested-name-specifiers.

[1] This is quite an inexact description. It’s hard to describe a grammar in plain English…