What does the single ampersand after the parameter list of a member function declaration mean?

Question

It means the member will be invoked when the object is an lvalue reference.

[C++11: 9.3.1/5]: A non-static member function may be declared with a ref-qualifier (8.3.5); see 13.3.1.

[C++11: 13.3.1/4]: For non-static member functions, the type of the implicit object parameter is

• “lvalue reference to cv X” for functions declared without a ref-qualifier or with the & ref-qualifier
• “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. [..]

(and some more rules that I can't find)

Without a ref-qualifier, the function can always be invoked, regardless of the value category of the expression through which you're invoking it:

struct foo
{
    void bar() {}
    void bar1() & {}
    void bar2() && {}
};

int main()
{
    foo().bar();  // (always fine)
    foo().bar1(); // doesn't compile because bar1() requires an lvalue
    foo().bar2();
    
    foo f;
    f.bar();      // (always fine)
    f.bar1();
    f.bar2();     // doesn't compile because bar2() requires an rvalue
}

Live demo ^{(thanks Praetorian)}

But what does the single ampersand mean?

The function can only be called on an lvalue, not on an rvalue.

How is it different than without the ampersand?

Without a ref-qualifier you can invoke the function on an lvalue or an rvalue.

With a ref-qualifier you can only call the function on the corresponding value category.

A function without a ref-qualifier can be called for both rvalue and lvalues. A function with a && ref-qualifier can only be called for rvalues. A function with a & ref-qualifier can only be called for lvalues.

class No { void foo(); };
class L { void foo() &; };
class R { void foo() &&; };

No().foo(); // valid
No no; no.foo(); // valid
L().foo(); // invalid
L l; l.foo(); // valid
R().foo(); // valid
R r; r.foo(); // invalid

Unfortunately, I can only find this rule in 5.5/6, which applies only to pointer-to-member dereference expressions. I know it applies otherwise too.

Furthermore, you cannot overload on ref-qualifier vs no ref-qualifier, see 13.1/2 bullet 3. You can overload on & vs &&.

(And due to my fruitless search of the standard, LRiO's answer now has all that info too.)