There can be many reasons why the market value of a corporation's stock is much greater than the amount of stockholders' equity reported on the balance sheet. Let's start by defining stockholders' equity as the difference between the asset amounts reported on the balance sheet minus the liability amounts. Next, the accountant's cost principle requires that only the cost of items purchased can be reported as an asset. This means that valuable trade names that were never purchased (but were developed over time) are not reported on the balance sheet. The same holds for a great management team and an amazing reputation. The cost principle also means that many long-term assets are reported at cost (and not at their current higher market value). Many plant assets are reported at minimal amounts because their costs have been reduced by the cumulative amount of depreciation taken over the years.
Other factors contributing to a high market value might be a corporation's earnings and dividends that are consistently growing and/or a special niche for its products or services that is recognized by the market.
Lastly, a corporation's stockholders' equity may have been reduced from the purchase of treasury stock at a high cost.