hey there!
maybe your webserver doesnt send out emails?
read this:
https://woocommerce.com/document/email-faq/
on one website i did a shop on i needed to use an extra plugin for email sending.
it was one of these i think
MailPoet (Plugin) – Send unlimited emails free per month (1,000 unique recipients limit).
Mailjet (Plugin) – Send 6,000 emails free per month.
Sendinblue (Plugin) – Send 9,000 emails free per day.
Postmark (Plugin) – Priced plans start at 10,000 emails a month.
Amazon SES (Plugin) – Send 62,000 emails free per month if your website is hosted on AWS or pricing starts at $0.10 for every 1,000 emails.