Appraisals provide an objective opinion of value, but it's not an exact science so appraisals may differ.
For buying and selling purposes, appraisals are usually based on market value - what the property could probably be sold for. Other types of value include insurance value, replacement value, and assessed value for property tax purposes.
Appraised value is not a constant number. Changes in market conditions can dramatically alter appraised value.
Appraised value doesn't take into account special considerations, like the need to sell rapidly.
Lenders usually use either the appraised value or the sale price, whichever is less, to determine the amount of the mortgage they will offer.