Interpolation is made possible by a principle called spatial autocorrelation. This is a fundamental principle based on Tobler’s first law of geography, which states that locations that are closer together are more likely to have similar values than locations that are farther apart.
An example is sea-surface temperature, for which one might expect a high degree of correlation between measurements taken close together. In the case of elevations, a simplistic interpolation function takes the elevation value of the nearest stored location and assigns this to the location that is not stored. Smarter interpolation functions, involving more than a single stored value, should be preferred.