Assessed value is a value based upon the physical characteristics and it's assigned by your taxing municipality.
Market value is an expected value based upon current conditions and comparable properties. It can and often does vary from assessed value and it does not mean that a home is "worth" that price. Market value fluctuates depending on the amount and quality of comparable data available when the home is evaluated. Actual market value can only be determined if the property were offered for sale and a sale consumated.