The term "market value" refers to the price an asset would fetch were it to be sold. This price is not necessarily equivalent to what the asset was purchased for, only what it is worth now. Since assets can fetch different prices if sold in different locations, an asset can have different market values in different markets. For the purposes of investors, this value will usually be restricted to the value within a single market.
Sometimes, if an asset changes hands, its value changes. This is because the new owner may be able to fetch a higher price or leverage certain efficiencies that result from a transfer of the property. Alternately, the asset may be worth less if it changes hands. So, when deciding how much an asset is worth, an investor may attempt to calculate its "fair price," meaning how much a party wishing to buy it should pay for it. This fair price may be lower or higher than the market price, depending on how much it is worth to the party buying it.
An asset's fair value is often equivalent to its market value. For example, if one company purchasing another company would not have a special advantage or disadvantage if it were to sell that asset right away, and both companies can freely sell the asset on the open market, then the fair value for the asset is the same as its market value. However, more often, one company will hold a slight advantage, meaning the values will differ.