Emails are sent using your internal email server in WordPress, make sure you have it setup. Our plugin is not sending the emails, it just tells wordpress what needs to be sent and wordpress takes care of it. So if it does not work – it means your email server is not setup. Please check with your hosting support.
You can use this plugin to test if your mail server is working: https://wordpress.org/plugins/check-email/
Sometimes some mail servers don’t send emails to the same domain, so if you are testing bookings with a user who has the same email address as your WordPress mail server.