Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.
But it typically does not make sense to talk about generalizing to a larger population of such units.
Clinical trials also typically use convenience samples, however the aim is often to make inferences about the effectiveness of treatments in other patients, and given the inclusion and exclusion criteria for some clinical trials, the sample may not be representative of the majority of patients with the condition or disease.
For example, if blood pressure measurements are made daily for a week on each subject in a study, there would be seven data values for each statistical unit.
Ignoring these dependencies, the analysis can lead to an inflated sample size or pseudoreplication.