Confirm it was sent
Settings → Notifications → History shows every message and whether it was delivered. The same record is on the appointment and the client.
If it was sent
Ask the customer to check spam and promotions, and confirm the address on the booking is spelled correctly. Corporate mail filters are a common cause.
If it was not sent
Check the message is turned on under Settings → Notifications, and that the booking has an email address at all — appointments added by phone sometimes do not.
Your own alerts
Same checks, using the email on your account under Settings → Account.