A piece of data used in public key cryptography (specifically public key infrastructures) that contains identifying information (i.e. email address or web address), a hash of a public key, and a digital signature that authenticates the data in the certificate. For questions specifically about [x509], [certificate-authority], or [public-key-infrastructure], please use those tags.
Also commonly known as a digital certificate, a certificate is a piece of data issued by a Certificate Authority for the purpose of associating a public key with a person, account, organization, or machine.
Most certificates are in the X.509 format, defined in RFC2459, though there are other less-used formats, such as the EAC Certificate format for Electronic Travel Documents (aka "ePassports").
Certificates are most commonly used for server authentication during the TLS handshake by allowing the server to issue trusted signatures, though certificates are also commonly used in corporate and governmental settings for signing and encrypting email and other documents, as well as in embedded chips in smartcards and ID badges for providing physical and logical access to computer systems and restricted locations.