A first-party claim is a claim that you have with your own insurance company. So, you’re the named insured, you got the policy written for you, you’re paying premiums on the policy, and now you want to get compensation for a claim that you have under your insurance policy on your property. So, you have a first-party claim, meaning it’s with you, and your insurance company.
It’s different than a third-party claim, which would be you against someone else that’s covered under their insurance policy. Say, for example, in a car accident. If somebody hits you and they have insurance coverage, you would bring a claim against that person’s insurance company. That would be a third-party claim. A first-party claim is just you with your insurance company.