The role of certificates in secure online transactions is to authenticate the identity of a website and enable encryption of data transmitted between the server and clients. Certificates are issued by trusted entities known as Certificate Authorities (CAs). When a user visits a secured website, the web server presents its certificate, which the browser verifies. If valid, a secure connection is established via the HTTPS protocol, ensuring that data remains confidential and protected from interception during transmission, fostering trust in online transactions.