You need a domain name and a host with PHP and MySQL. Most hosts come with these features, so if yours doesn’t, you can shop around. If you already have a website and just want the booking software, we can do that, too!
If you run a business website, you should have an SSL certificate for your site. This means that any information submitted will be sent encrypted and is much harder to be intercepted by a third-party. This is highly recommended as it will give your visitors and customers a sense of security, and is required if you are collecting sensitive data, such as credit card details. Your host will be able to help you with this.