Local realism is the scientific paradigm that is used, almost exclusively, for understanding how the universe works. Objects and forces move and interact in sensible ways, even though we may not fully understand those ways. Causality works. When things interact over a distance, there is a sensible rule for how the distance affects the interaction, for example, and inverse-square rule.
Scientists wouldn't need a term for something this straightforward if it weren't for the fact that, at microscopic scales, the universe is ruled by quantum mechanics, and, under quantum mechanics, local realism is not obeyed. The state of a system is determined by the DeBroglie wave function and the Heisenberg Uncertainty Principle. You can't know a particle's exact position, for example; all you can know is a probability distribution for it. But, as soon as you make a precise measurement, the wave function "chooses" an exact value, complying with the probability, and "collapses" to a function specifying that value exactly. The "conjugate" attribute (position vs. momentum, for example) then becomes completely unspecified. This has the non-intuitive consequence that observing something actually changes it. The human mind seems to enter into the behavior of the universe, a rather unsettling prospect. At the extreme and fanciful level, one could ask the question "Does the moon exist if no one is looking at it?"
One attempt to escape this situation was proposed quite early on—particles actually have precise positions and momenta somehow encoded into them invisibly. The wave function just tells how that "hidden" information will express itself when the attribute is measured. But very careful experiments, early in the history of quantum mechanics, showed that hidden variable theories don't work.
Other very careful analyses and careful experiments, particularly the result of Bell's theorem, showed unequivocally that, when local realism conflicts with strict (Copenhagen) quantum mechanics, the latter is correct.
The most notorious consequence of the failure of local realism is the phenomenon of action at a distance.
- Of course we're always "looking" indirectly; we would be aware of the Earthquake that would result if the Moon's tidal effect were to disappear.