Terms and conditions is one of those phrases people have learned to scroll past in every context, which is unfortunate in the case of pet insurance because the terms and conditions contain things that actually matter.
In a pet insurance context the terms and conditions cover things like your obligation to provide accurate information when you apply, your responsibility to tell the insurer about changes in your circumstances, what you must do when making a claim (including time limits for submitting claims and what evidence you need to provide), what counts as a valid claim and the grounds on which the insurer can refuse or reduce a payout.
They also cover the insurer's rights, things like their ability to change the terms at renewal, their rights around cancellation and their approach to fraud.
The terms and conditions are usually part of the policy booklet rather than a separate document, though some insurers present them separately. The definitions section, the exclusions section and the claims conditions section are the parts with the most practical relevance for most policyholders.
Most disputes between pet owners and insurers that end up going to the ombudsman come down to a difference of interpretation of the terms and conditions, often because the policyholder didn't know a particular requirement existed. That's not always the policyholder's fault, some policy terms are not made clear enough at the point of sale, but reading the key sections before you need to make a claim puts you in a much stronger position.