Generically, a certificate of insurance is a form populated by your insurance carrier or insurance agent. The certificate identifies what insurance you have; specifically, the dates, basic coverage limits, and insurance carrier for your policy.
Sometimes the company requesting the certificate may want additional information beyond dates, basic coverage limits, and insurance carrier. They may want proof that they are an additional insured, that the policy grants you the right to waive your right to subrogation, or that they will receive a notice if the policies cancel. If they request this, you need to first ensure that your policy actually gives them these rights and privileges. Then your carrier and agent can either provide them a copy of the endorsement or can describe those endorsements in a special section of the form.
The key thing to understand about certificates of insurance is that they do not override the coverages of your policy. If there is a conflict between the policy and the certificate, the policy will always win.