Levy flights model activities that involve a lot of small steps, interspersed with occasional very large excursions.

Examples include
foraging paths of some deer and albatross, and games of hide-and-seek.

In the case of foraging paths, this result is sensible because the stopping points of a Levy flight are fractal(scale invariant is the main point here), and in complex ecosystems the distribution of food is fractal.

Fractal distribution of food means there are some large areas without food.

To avoid spending too much time in such unproductive areas, animals need to develop search strategies that generate a fractal distribution of stopping points. Levy flights have this property.

As to why hide-and-seek is well described by a Levy flight, recall how it is played
The seeker runs across the yard (long trip) to a spot with several plausible hiding places. That area is investigated (several short trips) until the possibilities are exhausted. Then the seeker runs across the yard (another long trip) to the next spot with several hiding places. To be sure, there are more small trips than large trips, but not that many more. Careful analysis yields (approximately) a power-law distribution of trip sizes.