The appraisal should match the market value of the home. All too often, though, Appraisers don't do a real appraisal, they just make sure the appraisal is enough to make the loan work. I re-financed a home a few years ago that had a market value of $300k. I was only re-financing half that amount, and (low and behold!!) the appraisal came in just above the refi amount, nowhere near the market value of the home. One of my pet peeves...if I am paying an Appraiser to appraise my property (regardless of reason), I EXPECT them to give me a reasonable assimilation of current market value!!
The bank, however, is just looking to see that the amount they are loaning on the property is supported by the appraised value. If the appraisal comes in too high...no problem, but if it's too low you'll have to make some decisions...get a second appraisal (at your expense), or make up the difference out of pocket. Whenever you're talking about "value" you are likely to have many correct answers. Market value may be VERY DIFFERENT than what a buyer might be willing to pay if they really MUST HAVE a certain home. Similarly, a seller who LOVES their home and raised their family there may feel the value is much higher than the market value suggest. None of those "values" are wrong. If a buyer feels his or her house is worth $500k and the market value is just $250k, and they will not sell for less than $500k, they are not very likely to sell it, because they would have to find a buyer who agrees that it's worth $500k, which probably isn't going to happen because most buyers will go buy the other houses on the market similar to it that are selling for $250k. But the seller has that prerogative.
While the Market Value should typically be expressed in a range (ie: $475k to $500k), it is a fairly scientific figure with a little bit of "art" thrown in. Where it gets tricky (and often more "artsy") is where there are no recent sales of similar homes to compare with. Very interesting subject, often clouded by emotion, and NEVER as simple and straight-forward as we would all like it to be! Best of luck with your purchase..