This class is used with the Theme Customization API to render the custom color selector control on the Theme Customizer in WordPress 3.4 or newer.
$wp_customize->add_control( new WP_Customize_Color_Control( $wp_customize, 'link_color', array( 'label' => __( 'Header Color', 'mytheme' ), 'section' => 'your_section_id', 'settings' => 'your_setting_id', ) ) );
For more information on available Theme Customizer controls, see the codex entry for WP_Customize_Manager->add_control()