Three approaches to value
There are three ways to determine the value of anything, and each plays a part in property appraisal.

The most widely-used and accepted in residential practice is the sales comparison approach.  This approach bases its opinion of value on what similar properties in the vicinity have sold for recently, with appropriate adjustments for time, acreage, living area, amenities and so on.  It is these adjustments where the expertise of the professional appraiser becomes necessary -- no computer can tell you how much or little to mark up for a fireplace without knowing the neighborhood or even talking to Realtors and recent buyers in the area about how important that amenity is in that particular location.

Another approach is the cost approach.  How much would it cost to purchase the land and rebuild the improvement, minus "accrued depreciation," that is, depreciation that has occurred since the property actually was built?  The cost approach includes concepts like "economic life" and "effective age" that are mostly of use in determining the value of special use properties, special purpose properties or properties where subsequent structural improvements greatly impact value. Generally, the cost approach is the highest of the three approaches to value, as no knowledgeable buyer would pay more for a property than he or she could build one of like utility for a lesser cost. 

The third approach to value is called the income approach.  Some properties generate income for their owners -- the most obvious examples being rental properties such as commercial strip-centers, office buildings, industrial buildings, apartment buildings, non owner-occupied houses and duplexes and the like.  The rental income an owner might reasonably expect from a property is part of its value.  For a purely owner-occupied residential property, this may not be applicable, but it can be important if the property is to be rented out or used otherwise to generate income, such as a storage facility, cell tower rental and office building.