$this->messageManager->addError(
   $this->_objectManager->get('MagentoFrameworkEscaper')->escapeHtml($message)
);

class Example
{
    protected $_messageManager;

    public function __construct(
        MagentoFrameworkMessageManagerInterface $messageManager
    ) {
        $this->_messageManager = $messageManager;
    }

    public function method( ) {
        ..
        $message = '...';
        $this->_messageManager->addError($message);
        ..
    }
}

$messages = $this->messageManager->getMessages(true);

$block = $this->layoutFactory->create()->getMessagesBlock();
...
$block->setMessages($this->messageManager->getMessages(true));
$resultJson = $this->resultJsonFactory->create();

return $resultJson->setData([
    'messages' => $block->getGroupedHtml(),
    'error' => $error
]);

class yourAction extends MagentoFrameworkAppActionAction
{
    /** var ... */
    protected $_messageManager;

    public function __construct(Context $context)
    {
        $this->_messageManager = $context->getMessageManager();
        parent::__construct($context);
    }

<referenceContainer name="page.messages">
    <block class="MagentoCheckoutBlockCartValidationMessages" name="checkout.cart.validationmessages"/>
</referenceContainer>

/**
 * Events listener
 */
$(document).on('ajaxComplete', function (event, xhr, settings) {
    var sections,
        redirects;

    if (settings.type.match(/post|put/i)) {
        sections = sectionConfig.getAffectedSections(settings.url);

        if (sections) {
            customerData.invalidate(sections);
            redirects = ['redirect', 'backUrl'];

            if (_.isObject(xhr.responseJSON) && !_.isEmpty(_.pick(xhr.responseJSON, redirects))) {
                return;
            }
            customerData.reload(sections, true);
        }
    }
});