Just as the name would suggest, in an observational study, scientists observe subjects and look for correlations between risk factors and outcomes, but they do not actively experiment on the subjects.
There are many kinds of observational studies, including case-control studies, cohort studies, and case series. An observational study may be a one-time survey, or it may follow a group of people for years or even decades.
Observational studies are often used as preliminary studies, but they can also be used where experimentation is unethical or impractical. For example, it would be unethical to randomly expose individuals to asbestos and follow their health over time. But a prospective cohort study of workers in a field where individuals are normally exposed to the toxic substance could provide useful information about its short- and long-term effects on health.
Not all observational studies are the same quality as some are much better than others. For example, a prospective cohort study that follows people over time can look for temporal associations between events, which can actually suggest causation, whereas a survey can only look for correlations since they are assessing a single point in time.