One of the first things the lender will do AFTER you have successfully passed this period, is to order the appraisal. The reason this usually occurs AFTER the inspection period is because if you run into a snag during your home inspection or the repair negotiations and decide to exit the contract, the lender does not want you to be liable for the cost of the appraisal, which is somewhere between $350 to $450. If things run smoothly, a good buyer's agent will alert the lender that the inspection period ended successfully as a cue to move forward and order the appraisal. (Note: There are times when the lender may move ahead with ordering the appraisal before the inspection has been completed, but these times would be relevant to the situation.)
An appraiser is an independent player in your home equation. Lenders can no longer talk with the appraiser or have any weigh in on which appraiser will be contacted to do your inspection. This is now all done through a 3rd party order system, to make sure that there is no collusion with any of the parties involved. The appraiser is randomly pulled from a pool of inspectors. Once the appraisal is ordered, the appraiser will schedule a time to come to the property alone. Buyers are not present for this.
After the appraiser is finished, he/she will go back to the office to write up a full appraisal report, researching all the comps in the area and deriving what would be the most accurate market value for your home, usually based on the last 6 months of sales in the area. If the appraiser's final value is equal to or higher than the sales price of your property, you are good to go. If it is less than the sales price of your property, then we have a challenge. Your lender cannot lend on more than what the fair market value is on the home you are about to purchase. Therefore, your agent is notified right away and he/she would quickly notify the listing agent of the lower appraised value, usually providing the appraisal report (with the buyer's permission) to prove the lower amount. The seller should eventually agree to meet the appraiser's price even though he/she may be reluctant to do so, as the only other alternative to lowering the price is to just not sell the home at all. It's the seller's call, but of course, most sellers will move forward with the appraiser's value. The home was just priced a little too high for the current market and the appraiser called it out. As a buyer, you can rest assured that you are protected with a fair market value on your asset and will not be paying more for the asset than what it is currently worth. Appraisals are a good protection for your investment.
If you are a cash buyer, then you are not using a lender so an appraisal is not necessary to meet the guidelines of any loan. As a cash buyer you can forgo the appraisal if you want. Some cash buyers are very much aware of what the fair market price might be. But many cash buyers would benefit writing into their purchase offer a contingency for an appraisal that must be equal to or higher than the agreed sales price, just to satisfy themselves that they are, indeed, not paying too much for the property. There are exceptions to this, especially in the case of multiple bids where the cash buyer would like to absolutely win the bid, having no contingencies, so the seller might choose their offer over another. You can see that at this point, unless the cash buyer knows the market well, the seller benefits from this deal. In this scenario, the seller can march onward to the closing table, as he/she does not have to wait for an appraisal to be completed to make sure their price meets market value, nor do they need to wait and see if their buyer can make it through underwriting successfully. Cash deals can usually close in just a few weeks, in contrast to a buyer with a loan that will take 35 to 45 days to close on average. You can see why the phrase, "Cash is King", rules in the buying market.