A waiting period is the short time at the start of a new policy when certain claims, usually illness claims, are not covered yet.
Nearly all pet insurance policies have a waiting period built in and its one of the things people find out about at the worst possible moment, when a claim gets refused. So its worth knowing about before you need it.
The most common version is a 14 day waiting period for illness. That means any illness that starts within the first 14 days of your policy wont be covered, even if you took the policy out weeks in advance. The clock runs from the date the policy starts, not the date your pet comes home, not the date you paid, not the date the documents arrived.
Waiting periods for accidents are usually shorter, sometimes just 24 to 48 hours, because accidents are clearly unforeseeable in a way that illness sometimes isn't.
The thing that catches people out most often is the timing. You might have been really organised, sorted insurance out a month before bringing your puppy home, and then found that symptoms appearing in the first week or two after the policy start date still fall inside the waiting period. The claim gets refused and it feels completely unfair, but the terms are usually clear even if they weren't explained well at the point of sale.
Some conditions have their own specific waiting periods that are longer than the standard one. Cruciate ligament problems for example are sometimes subject to a six month waiting period on certain policies, because they're so common in certain breeds. Its a policy detail to check the policy wording for anything specific to your pet's breed before you assume the standard 14 days applies to everything.
If a claim is refused because of a waiting period its worth asking the insurer to confirm exactly what is excluded and for how long. In some cases, if the condition fully resolves and there's no recurrence, it may be possible for it to be covered again in the future.