A Digital Certificate is a public key which certifies, by signing, that some data is owned by certain Private Key.
The digital certificate allows entities to share their public key so the data can be verified that comes from them and no other entity.
The Public Key is created by a Private Key and used to sign or decrypt/encrypt data. Eg: Alice emails Bob, but before sending the message uses one of her private key to encrypt it. The public key is created after hashing the message. The result is a public key which can be used by Bob to decrypt the message and certify it comes from Alice and it has not been modifies.
One of the most common use for the DC is by major websites to assure the users their contents have not been changed, and to share keys for encrypting and decrypting web content.
A CA is a trusted third party which enables individuals to increase their trustworthiness by certifying them.
eg: A Goverment makes you to go a its TaxOffice to issue you a digital certificate after you demonstrate you are who you say you are, then their provide you with a DC to grant you access to other websites which thust the goverment, so they don’t need to double check your identity.