Consider a (very) simple calculator class :

class calculator
{
public:
    int add( int a, int b );
};

Obviously writing unit tests for such a class is trivial, one of them could be :

BOOST_AUTO_TEST_CASE( zero_plus_zero_is_zero )
{
    calculator c;
    BOOST_CHECK_EQUAL( 0, c.add( 0, 0 ) );
}

What now if the calculator class looks more like this :

class view
{
public:
    virtual void display( int result ) = 0;
};

class calculator
{
public:
    calculator( view& v );

    void add( int a, int b ); // the result will be sent to the view 'v'
};

Writing unit tests becomes a bit more tedious and requires some boiler-plate code, for instance :

class my_view : public view
{
public:
    my_view()
        : called( false )
    {}
    virtual void display( int result )
    {
        called = true;
        value = result;
    }
    bool called;
    int value;
};

BOOST_AUTO_TEST_CASE( zero_plus_zero_is_zero )
{
    my_view v;
    calculator c( v );
    c.add( 0, 0 );
    BOOST_REQUIRE( v.called );
    BOOST_CHECK_EQUAL( 0, v.value );
}

Mock objects main purpose is to alleviate the user from the burden of writing all this boiler-plate code.

Here is how the last test can be rewritten using a mock object :

BOOST_MOCK_BASE_CLASS( mock_view, view ) // declare a 'mock_view' class implementing 'view'
{
    BOOST_MOCK_METHOD( display, 1 )      // implement the 'display' method from 'view' (taking 1 argument)
};

BOOST_AUTO_TEST_CASE( zero_plus_zero_is_zero )
{
    mock_view v;
    calculator c( v );
    BOOST_MOCK_EXPECT( v.display ).once().with( 0 ); // expect the 'display' method to be called once (and only once) with a parameter value equal to 0
    c.add( 0, 0 );
}

and all the checks are automatically handled by the library.