“Notify contact on case close” should be enabled so that the email notification will be sent when the Case is closed.

Steps:

1. Create an Email Template.

Sample Email Template:

Hello {!Contact.Name},

Your Case:{!Case.CaseNumber} is closed.

Thanks,
Admin

2. Add the Email Template in Support Settings. Go to Support Settings in Salesforce Setup. Edit it and select the Email Template for Case Close Template.

3. Go to Object Manager. Select the Case object. Click Case Close Page Layouts. Enable “Notify contact checkbox” using the Layout Properties button.

Output: