A property's assessed value is determined by a public tax assessor for the purposes of taxation. It is good to know what percent of valuation your city or town uses to determine tax rate. You can find this out by looking at your tax bill or contacting your town or city assessors office. The New York State Office of Real Property Services has plenty of information on assessed value.
Market value, which is not the same as assessed value, is the agreed upon price between a fully informed, willing buyer and a fully informed, willing seller, neither party being under duress (such as divorce or relocation).
Differences between the two will vary as the market value shifts. If the market value for your area climbs on a steady basis your locality my reassess everyone (thereby increasing property tax revenue). If the market value declines steadily you may want to petition your assessor's office for a change in assessed value. Your property may also be reassessed if you do home improvements which require a permit.