A certificate authority or certification authority (CA) is an entity that stores, signs, and issues public key certificates.
The certificate authority (CA) acts as a 'trusted third party' for the communicating users and, using cryptographic binding methods (e.g., digital signatures) represents to both parties involved that the public keys each holds which allegedly belong to the other, actually do so.
A digital notary service, if you will.
Such CAs can be private organizations providing such assurances, or government agencies, or some combination of the two.
One particularly common use for certificate authorities is to sign certificates used in HTTPS.