A no-reply email is one that has been sent from an email address that routes to an inbox or area of the server that is not regularly checked. Emails sent to the no-reply address will not receive a response.
No-reply emails are generally used to send communications that do not warrant a response from the recipient, such as purchase invoices or promotional email blasts. These types of emails can be identified by the sender's address, which often has some variation of "no reply" or "do not reply" in the name field. There is also usually a line in the body of the email warning recipients not to respond directly.