When should you use 'friend' in C++?

At work we use friends for testing code, extensively. It means we can provide proper encapsulation and information hiding for the main application code. But also we can have separate test code that uses friends to inspect internal state and data for testing.

Suffice to say I wouldn't use the friend keyword as an essential component of your design.

The friend keyword has a number of good uses. Here are the two uses immediately visible to me:

Friend Definition

Friend definition allows to define a function in class-scope, but the function will not be defined as a member function, but as a free function of the enclosing namespace, and won't be visible normally except for argument dependent lookup. That makes it especially useful for operator overloading:

namespace utils {
    class f {
    private:
        typedef int int_type;
        int_type value;

    public:
        // let's assume it doesn't only need .value, but some
        // internal stuff.
        friend f operator+(f const& a, f const& b) {
            // name resolution finds names in class-scope. 
            // int_type is visible here.
            return f(a.value + b.value);
        }

        int getValue() const { return value; }
    };
}

int main() {
    utils::f a, b;
    std::cout << (a + b).getValue(); // valid
}

Private CRTP Base Class

Sometimes, you find the need that a policy needs access to the derived class:

// possible policy used for flexible-class.
template<typename Derived>
struct Policy {
    void doSomething() {
        // casting this to Derived* requires us to see that we are a 
        // base-class of Derived.
        some_type const& t = static_cast<Derived*>(this)->getSomething();
    }
};

// note, derived privately
template<template<typename> class SomePolicy>
struct FlexibleClass : private SomePolicy<FlexibleClass> {
    // we derive privately, so the base-class wouldn't notice that, 
    // (even though it's the base itself!), so we need a friend declaration
    // to make the base a friend of us.
    friend class SomePolicy<FlexibleClass>;

    void doStuff() {
         // calls doSomething of the policy
         this->doSomething();
    }

    // will return useful information
    some_type getSomething();
};

You will find a non-contrived example for that in this answer. Another code using that is in this answer. The CRTP base casts its this pointer, to be able to access data-fields of the derived class using data-member-pointers.

Firstly (IMO) don't listen to people who say friend is not useful. It IS useful. In many situations you will have objects with data or functionality that are not intended to be publicly available. This is particularly true of large codebases with many authors who may only be superficially familiar with different areas.

There ARE alternatives to the friend specifier, but often they are cumbersome (cpp-level concrete classes/masked typedefs) or not foolproof (comments or function name conventions).

Onto the answer;

The friend specifier allows the designated class access to protected data or functionality within the class making the friend statement. For example in the below code anyone may ask a child for their name, but only the mother and the child may change the name.

You can take this simple example further by considering a more complex class such as a Window. Quite likely a Window will have many function/data elements that should not be publicly accessible, but ARE needed by a related class such as a WindowManager.

class Child
{
//Mother class members can access the private parts of class Child.
friend class Mother;

public:

  string name( void );

protected:

  void setName( string newName );
};