It seems so simple. You have an accident so you present your insurance company with a claim and walk away with a check to do the necessary repairs. Maybe in a perfect world, but in the real world it doesn't work quite that way. Body shop estimates play a significant role in that scenario and can often have an affect on your next car insurance quote.
Some insurance companies will send a claims adjuster to determine the extent of the damage to your car and what the cost will be to fix it. Some companies request one or more body shop estimates to arrive at the cost of repair. From this point on a few different things can happen. How the money gets from the insurance company to you or to the repair shop often depends on whether it is coming from your insurer or someone else. There are no laws that govern how these claims are processed or how payments are made but if your carrier is not paying the claim there will be no increase in your next car insurance quote. That is a very good thing.
Your insurance company can write a check directly to you that can be used to repair the damage or spent in any way you choose. Although the check is intended for damage repair there is no specific wording in the policy that forces you to use it that way. Whatever you do with the money, as far as the insurance company is concerned, it paid a claim and that will show up in your car insurance quote when it is time to renew your policy. One possible problem with this method of payment is that once the check is cashed, you will be personally responsible for any additional charges that may result as the repair work begins. They are called estimates and not quotes for a reason.
Another possibility is that the insurance company sends a check to the body shop for payment in full when the repairs have been completed. The body shop estimates are sent directly to the insurer or to you who then passes it along to your agent. This creates a relationship between the people doing the work and the people paying the bill leaving you out of the equation. This is a good way to prevent surprise expenses and eliminate the need for any unnecessary involvement on your part. Another reason to allow the insurance company to deal with the repair shop is that many companies have pre-approved arrangements. The insurance company is less likely to fuss over a body shop estimate that comes from a shop it has worked with previously.