Most Pet Insurance actually Reimburses you for the cost of the vet visit so you would traditionally pay out the cost for the Vet Visit and then make a claim and the Pet Insurance Company then pays you back once you make the Claim.
However some Pet Insurance companies now do pay the Vet Directly so you don't have to pay out of pocket and then wait for Reimbursement from the Pet Insurance Company.
Trupanion is one pet insurance company that does pay the vet directly so you can get your pet the treatment it needs instead of having to pay out of pocket when you may not have the money.