Insurance companies don't want to spend more on repairing your vehicle than necessary. One of the ways they can do this is by authorizing repair facilities to use parts that were not made by the original equipment manufacturer, or OEM. These are the automotive equivalent to generic product in the grocery store; they are made with the same standards as the original parts but are often more competitively priced. Many people disapprove of using these parts, called aftermarket parts, but independent research has not been able to determine any significant difference in performance or safety between using OEM parts and generic replacements.
If you insist on using OEM parts, you may have to pay a portion of the bill. Many insurance companies will only pay the non-OEM price for the parts, and if you want more expensive OEM parts you will have to pay the difference in costs. In most cases, the cost to you will not be a huge one, but there are some situations where the use of OEM parts could double the cost. It can be difficult to find OEM parts for older vehicles. Realistically, as the car ages it will lose value and whether or not OEM parts are used becomes an academic point. No matter what price you are willing to pay, if the only solution is to have a part fabricated, that is the choice you will have to take.
Read your policy. If your insurance company has a regular policy of authorizing aftermarket parts, it will be listed in the policy. If you are not able to find reference to OEM equipment in your policy, call the insurance company and ask them to clarify their stance.