The function of a digital certificate in internet security is to authenticate the identity of an entity, such as a website or organization, and establish secure connections. Digital certificates, issued by trusted Certificate Authorities (CAs), contain a public key and the identity of the holder. They help in encrypting data during transmission, ensuring confidentiality and integrity. When browsers interact with secure sites, they check the digital certificate to verify the legitimacy of the server, promoting trust in online communications and transactions.