In general use, a certificate is a document issued by some authority to attest to a truth or to offer certain evidence. A digital certificate is commonly used to offer evidence in electronic form about the holder of the certificate. In PKI it comes from a trusted third party, called a certification authority (CA) and it bears the digital signature of that authority.
A common use for a digital certificate is to associate or “bind” a person to a public key, which is contained in the certificate. The CA is asserting that this unique public key belongs to one individual; that individual is the person who holds the linked private key. Only the person who holds the private key can decrypt something that’s encrypted with the public key.
Digital certificates are also commonly used in electronic commerce, where the owner of a secure site will obtain a digital certificate that’s checked by a browser for a secure session. In this case, the CA is asserting that the public key belongs to the business; it’s bound to the domain. The information associated with this certificate is also used to set up an encrypted session so that others cannot see personal information like credit card numbers when they are in transit over the web.