A home's assessed value is the county's measure of the value of both the home and land, for tax purposes. The assessor needs to know how much everything is worth to accurately calculate your property-tax bill.
Your insurance policy often reflects a different figure from an assessed or appraised value. Your home is being insured for its replacement cost – that is, the cost to rebuild the home.
An assessed or appraised value will adjust for depreciation, reducing your home's value due to age and wear and tear. Assessed values often are based on data from the prior year which, when combined with depreciation, will be a poor gauge of the home's reconstruction cost. An appraisal takes into account depreciation and other market factors as well, so that isn't a good guide for the replacement cost either.
Your insurance policy factors in labor and material costs, the age of the structure, geography, and ease of access to the site when calculating the replacement cost.