As with anything, the 'value' is what a willing and able seller and a willing a able buyer agrees to. An appraiser attempts to determine the most likely price for something (in this case a home) within reasonable amount of marketing time. The appraisal report will usually specify the expected marketing time. I think in most areas this will be 3-6 months, some areas longer and others shorter, depending on the market.
Of course, appraisals effect prices, because most buyers need to finance, and most financiers won't do it without an appraisal that is at least as much as the purchase amount. (That is the "able" part of the willing and able requirement).
Two appraisals performed on the same property at the same time can come back with very different numbers. I have bought two houses in the last 4 years- both had 2 appraisals done, and one the values were almost almost 17% different- a difference greater than most of the "errors" that the articles notes for Zestimate vs sale price. On the other house, the appraisals were came back with nearly identical values, but the first appraisal was done wrong. Still this value (the appraised value from both appraisals) was 16.2% higher than what I paid for the property.
My experiences are just as anecdotal as the articles, though. But I have spoken with real estate professionals all over the country that have the same experiences repeatedly with appraisals.
I paid a couple hundred bucks for an ex-general contractor with a thick binder to inspect my house for hours, looking inside the furnace heat exchanger and testing every wall outlet and inspecting the plumbing and roof inside and out and insulation and foundation and everything. That is a detailed analysis of what you're likely to spend on maintenance and upgrades over the next ten years. Its probably more useful than an appraisal but it takes a lot more time and money.
http://www.freddiemac.com/loanadvisorsuite/loancollateraladv... http://www.freddiemac.com/loanadvisorsuite/faq/loancollatera...
This doesn't even take into account the process for appraisal management companies (third parties).