Add to functions.php

function fishoa_add_checkbox($wp_customize){

    // Add section
    $wp_customize->add_section( 'fishoa_checkbox_section', array(
        'title' => 'My Custom Checkbox',
        'priority' => 10,
        'description' => 'Welcome to My Custom Checkbox section'
    ));

    // Add setting
    $wp_customize->add_setting( 'fishoa_checkbox', array(
        'default' => '',
    ));

    // Add control
    $wp_customize->add_control( 'fishoa_checkbox_control', array(
        'label' => 'Display Welcome Message',
        'type'  => 'checkbox',
        'section' => 'fishoa_checkbox_section',
        'settings' => 'fishoa_checkbox'
    ));

}
add_action( 'customize_register', 'fishoa_add_checkbox' );

In the view file, you need to create a variable for the checkbox

$showMessage  = get_theme_mod( 'fishoa_checkbox' );
$visible = no_visible; // name of the class for no visible

if( $showMessage == true ){
    $visible = is_visible; // name of the class for visible
}

After set the variable, you have to print it in the HTML tag

<div class="home <?php echo $visible; ?>">