What is the purpose of the "final" keyword in C++11 for functions?

What you are missing, as idljarn already mentioned in a comment is that if you are overriding a function from a base class, then you cannot possibly mark it as non-virtual:

struct base {
   virtual void f();
};
struct derived : base {
   void f() final;       // virtual as it overrides base::f
};
struct mostderived : derived {
   //void f();           // error: cannot override!
};

• It is to prevent a class from being inherited. From Wikipedia:

  C++11 also adds the ability to prevent inheriting from classes or simply preventing overriding methods in derived classes. This is done with the special identifier final. For example:

  struct Base1 final { };
  
  struct Derived1 : Base1 { }; // ill-formed because the class Base1 
                               // has been marked final
  

• It is also used to mark a virtual function so as to prevent it from being overridden in the derived classes:

  struct Base2 {
      virtual void f() final;
  };
  
  struct Derived2 : Base2 {
      void f(); // ill-formed because the virtual function Base2::f has 
                // been marked final
  };
  

Wikipedia further makes an interesting point:

Note that neither override nor final are language keywords. They are technically identifiers; they only gain special meaning when used in those specific contexts. In any other location, they can be valid identifiers.

That means, the following is allowed:

int const final = 0;     // ok
int const override = 1;  // ok

"final" also allows a compiler optimization to bypass the indirect call:

class IAbstract
{
public:
  virtual void DoSomething() = 0;
};

class CDerived : public IAbstract
{
  void DoSomething() final { m_x = 1 ; }

  void Blah( void ) { DoSomething(); }

};

with "final", the compiler can call CDerived::DoSomething() directly from within Blah(), or even inline. Without it, it has to generate an indirect call inside of Blah() because Blah() could be called inside a derived class which has overridden DoSomething().