Let's imagine that you want to study differences in risk taking behavior between teenage boys and girls. You might choose to observe behavior in a few different settings, such as on a sledding hill, a rock-climbing wall, an ice-skating rink and a bumper car ride. After you operationally define "risk-taking behavior," you would then observe teens in these settings and record every incidence of what you define as a risky behavior.
Some famous examples of naturalistic observations include Charles Darwin's journey aboard the HMS Beagle, which served as the basis for his theory of natural selection, and Jane Goodall's work studying the behavior of chimpanzees.