The certificate of insurance is essentially your proof of cover. It confirms that a policy exists, who it covers, what pet it relates to, the policy start and end dates and the level of cover in place.
For pet insurance its most commonly needed when a vet practice asks for proof that an animal is insured, or when you're making a claim and the insurer needs to verify the policy details. Some boarding kennels or dog walkers may also ask to see it.
Its not the same as the policy booklet. The certificate summarises the key facts of your cover in a brief format. The policy booklet contains all the detail. Both matter but for different purposes.
Your certificate of insurance should be included in your policy documents when cover starts. Most insurers now issue them digitally and they'll be in your online account or emailed to you alongside the other policy paperwork. If you can't find yours, your insurer can reissue it, usually straightaway through their online portal or by calling them.
Its worth keeping it somewhere accessible. If you need to show a vet that your pet is insured at short notice, being able to find it quickly saves a lot of stress.