Difference between private, public, and protected inheritance

To answer that question, I'd like to describe member's accessors first in my own words. If you already know this, skip to the heading "next:".

There are three accessors that I'm aware of: public, protected and private.

Let:

class Base {
    public:
        int publicMember;
    protected:
        int protectedMember;
    private:
        int privateMember;
};

• Everything that is aware of Base is also aware that Base contains publicMember.
• Only the children (and their children) are aware that Base contains protectedMember.
• No one but Base is aware of privateMember.

By "is aware of", I mean "acknowledge the existence of, and thus be able to access".

next:

The same happens with public, private and protected inheritance. Let's consider a class Base and a class Child that inherits from Base.

• If the inheritance is public, everything that is aware of Base and Child is also aware that Child inherits from Base.
• If the inheritance is protected, only Child, and its children, are aware that they inherit from Base.
• If the inheritance is private, no one other than Child is aware of the inheritance.

class A 
{
    public:
       int x;
    protected:
       int y;
    private:
       int z;
};

class B : public A
{
    // x is public
    // y is protected
    // z is not accessible from B
};

class C : protected A
{
    // x is protected
    // y is protected
    // z is not accessible from C
};

class D : private A    // 'private' is default for classes
{
    // x is private
    // y is private
    // z is not accessible from D
};

IMPORTANT NOTE: Classes B, C and D all contain the variables x, y and z. It is just question of access.

About usage of protected and private inheritance you could read here.