What does the & (ampersand) at the end of member function signature mean?

Ref-qualifiers - introduced in C++11

Ref-qualifiers is not C++17 feature (looking at the tag of the question), but was a feature introduced in C++11.

struct Foo
{
  void bar() const &  { std::cout << "const lvalue Foo\n"; }
  void bar()       &  { std::cout << "lvalue Foo\n"; }
  void bar() const && { std::cout << "const rvalue Foo\n"; }
  void bar()       && { std::cout << "rvalue Foo\n"; }
};

const Foo&& getFoo() { return std::move(Foo()); }

int main()
{
  const Foo c_foo;
  Foo foo;

  c_foo.bar();            // const lvalue Foo
  foo.bar();              // lvalue Foo
  getFoo().bar();         // [prvalue] const rvalue Foo
  Foo().bar();            // [prvalue] rvalue Foo

  // xvalues bind to rvalue references, and overload resolution
  // favours selecting the rvalue ref-qualifier overloads.
  std::move(c_foo).bar(); // [xvalue] const rvalue Foo
  std::move(foo).bar();   // [xvalue] rvalue Foo
}

Note that an rvalue may be used to initialize a const lvalue reference (and in so expanding the lifetime of the object identified by the rvalue), meaning that if we remove the rvalue ref-qualifier overloads from the example above, then the rvalue value categories in the example will all favour the remaining const & overload:

struct Foo
{
  void bar() const & { std::cout << "const lvalue Foo\n"; }
  void bar()       & { std::cout << "lvalue Foo\n"; }
};

const Foo&& getFoo() { return std::move(Foo()); }

int main()
{
  const Foo c_foo;
  Foo foo;

  // For all rvalue value categories overload resolution
  // now selects the 'const &' overload, as an rvalue may
  // be used to initialize a const lvalue reference.
  c_foo.bar();            // const lvalue Foo
  foo.bar();              // lvalue Foo
  getFoo().bar();         // const lvalue Foo
  Foo().bar();            // const lvalue Foo
  std::move(c_foo).bar(); // const lvalue Foo
  std::move(foo).bar();   // const lvalue Foo
}

See e.g. the following blog post for for a brief introduction:

• Andrzej's C++ blog - Ref-qualifiers

---

rvalues cannot invoke non-const & overloads

To possibly explain the intent of your recollected quote from the CppCon talk,

"... that the only true way of overloading operator= ..."

we visit [over.match.funcs]/1, /4 & /5 [emphasis mine]:

/1 The subclauses of [over.match.funcs] describe the set of candidate functions and the argument list submitted to overload resolution in each context in which overload resolution is used. ...

/4 For non-static member functions, the type of the implicit object parameter is

• (4.1) — “lvalue reference to cv X” for functions declared without a ref-qualifier or with the & ref-qualifier

• (4.2) — “rvalue reference to cv X” for functions declared with the && ref-qualifier

where X is the class of which the function is a member and cv is the cv-qualification on the member function declaration. ...

/5 ... For non-static member functions declared without a ref-qualifier, an additional rule applies:

• (5.1) — even if the implicit object parameter is not const-qualified, an rvalue can be bound to the parameter as long as in all other respects the argument can be converted to the type of the implicit object parameter. [ Note: The fact that such an argument is an rvalue does not affect the ranking of implicit conversion sequences. — end note ]

From /5 above, the following overload (where the explicit & ref-qualifier has been omitted)

struct test
{
    test& operator=(const test&) { return *this }
}

allows assigning values to r-values, e.g.

int main()
{
    test t1;
    t1 = test(); // assign to l-value
    test() = t1; // assign to r-value
}

However, if we explicitly declare the overload with the & ref-qualifier, [over.match.funcs]/5.1 does not apply, and as long we do not supply an overload declared with the && ref-qualifier, r-value assignment will not be allowed.

struct test
{
    test& operator=(const test&) & { return *this; }
};

int main()
{
    test t1;
    t1 = test(); // assign to l-value
    test() = t1; // error [clang]: error: no viable overloaded '='
}

I won't place any opinion as to whether explicitly including the & ref-qualifier when declaring custom assignment operator overloads is "the only true way of overload operator=", but would I dare to speculate, then I would guess that the intent behind such a statement is the exclusion of to-r-value assignment.

As a properly designed assignment operator should arguably never be const (const T& operator=(const T&) const & would not make much sense), and as an rvalue may not be used to initialize a non-const lvalue reference, a set of overloads for operator= for a given type T that contain only T& operator=(const T&) & will never proviade a viable overload that can be invoked from a T object identified to be of an rvalue value category.

As per http://en.cppreference.com/w/cpp/language/member_functions the & following your member function declaration is lvalue ref-qualifier.

In other words, it requires this to be an l-value (the implicit object parameter has type lvalue reference to cv-qualified X). There is also &&, which requires this to be an r-value.

To copy from documentation (const-, volatile-, and ref-qualified member functions):

#include <iostream>
struct S {
  void f() & { std::cout << "lvalue\n"; }
  void f() &&{ std::cout << "rvalue\n"; }
};

int main(){
  S s;
  s.f();            // prints "lvalue"
  std::move(s).f(); // prints "rvalue"
  S().f();          // prints "rvalue"
}