The "appraiser" is meant to locate a small number of comparable recent sales, apply adjustments for differences in property features and quality (such as more/less bathrooms, kitchen quality, condition, location and square footage), average the results and come up with a value for the property.
This is the value used in computing the loan-to-value ratio; if it comes in below sale price, the sale is likely to fall through (or the sale price may be renegotiated; appraisal is a contingency on the property transfer contract).
When I purchased my house, I was dealing with two potential lenders, so I asked each of them which appraisers would be acceptable to them, and then directly contacted the appraiser and once the appraisal was done, provided the report to both lenders. The report contained all the relevant calculations, and then gave a value which exactly matched the listing price of the property.
When I refinanced my loan, approximately a year after purchase (the interest rates had dropped quite a long way), the appraisal again included very precise calculations and pages of pictures and justification, and came to the conclusion that the value was exactly what I had paid for the property.
Now, I'm in the late stages of purchasing some vacant land. The appraisal was ordered by the bank, and the bank informed the appraiser of the pending purchase price. The value? Exactly the proposed purchase price.
This is not a science of exactly calculating property values. It is an art of manipulating numbers to match a desired outcome.
In the wake of the WaMu failure, there was talk about appraisers who had been giving artificially high values to properties, resulting in borrowers trapped in loans with properties they could not sell, or on better loan terms than they should be (since the loan to value ratio was artificially high; since US banks sell loans to underwriters, it is in their interest to manipulate the situation to make loans look more attractive than they really are). I was under the mistaken impression that the fall-out from this was that appraisers were to produce more accurate property appraisals. However, it seems that they continue to produce manipulated reports. In the case of the property I am in the process of purchasing, the realtor claims that the appraiser mentioned to him several times that the property was "great value" and had "amazing views" given the price.