After the validity period of a certificate it will automatically expire, unless you renew it manually. During it's validaty the certificate can be revoked by the CA (the issuer).
When should you revoke a certificate?
If the certificate's private key gets compromised by for instance a hack or a virus, it's advisable to revoke the certificate immediately. Other reasons could be the discontinuance of a a service or when the certificate may not be used anymore. If you lose the certificate's private key you may reissue the certificate with a new private key. After a reissue, the old certificate will not be automatically revoked.
Note: A revocation is not a cancellation and credit. Certificates can be cancelled within 30 days after issuance, by sending a seperate request per email.
How can you revoke a certificate?
Navigate in the Control Panel to the Certificates tab, and click on the certificate concerned. Under 'Actions' you can request a revocation. You will receive a confirmation of this request by e-mail, after which the certificate will be revoked within a few hours (maximum 24 hours). As soon as the certificate has been revoked, it won't be shown anymore.