Market value is how much your house is worth in the real estate market right now. This number comes from recent sales and homes on the market. This is what the appraiser is going to look at when placing a value on your home.
A good example of tax values and homes sales as follows.
I took 6 homes in the same subdivision. All are the exact same floorplan and all built within 1 year of each other. I looked at each tax value and found that each home had big differences in tax values some up to $50,000 different. This is crazy. It depended on who did the tax valuation at that specific time. Now all the homees that I took had sold over the past year. Each of these homes sold for far less than their tax value and all had essentially the same price per square footage sales price give or take a few thousand.
Don't get caught up in market value and tax value, however you will want to know if your tax value is really high as you may wish to find another home that has more reasonable taxes.