Betterment when speaking about auto insurance terms is referred to as a condition relating to original equipment, or older parts, on your automobile, when having been damaged in an accident may being replaced with new part(s). The resulting improved condition of the vehicle is known as betterment. Consequently many insurers may ask the insured to contribute to the cost of the repair if newer parts are used since they are improving the condition of your car.
It will depend upon state laws and insurance company guidelines but normally if you want better parts or newer parts than what the insurance company is offering to pay for you may be able to receive them if you are willing to pay the difference between the used parts an insurer is willingly to pay for.
As we mentioned, state laws do differ regarding betterment. Below is an example of how the state of Wisconsin's insurance regulator says about both betterment and the depreciation of car parts.
The WI Office of the Commissioner of Insurance states that betterment means that your repaired vehicle is better than it was before it was damaged. Your insurance company may only reduce your settlement if your vehicle's resale value has increased over what it was before the accident. Generally, an insurer will deduct the difference between the cost of a used part (appropriate for age and condition of the vehicle) and the cost of a new part. Betterment is only considered for major parts such as transmissions or engine blocks. Betterment might be considered for other parts that if new would improve the value or saleability of the vehicle.
Depreciation refers to a reduction in your settlement based on the age or use of a part that is to be replaced. Certain parts on your vehicle have a "life expectancy" and your insurance company may take this into consideration. For example, if a tire on your vehicle is expected to last 60,000 miles, but it was used for 30,000 miles at the time of the accident, your insurance company may elect to pay only 50% for a new tire.
In most all states during the repair process insurance companies will not typically pay for parts that are better than the parts being repaired or replaced on a vehicle. A car insurance company's repairs should make you whole, not better than you were before the accident. So in basic terms replacing car parts with better or more expensive parts would be what is known as "betterment" in regards to car insurance claims.