The classic example of externalities is pollution, but that's not especially creative. Instead, let's consider the vaccines that public health departments offer to children and older citizens (flu shots). The immunizations are usually free of a monetary charge, which is a benefit to the people who get vaccinated without having to pay. However, these people still might incur a cost in terms of discomfort at the site where the vaccine is injected, or a feeling of sickness for a day or two.

There is a benefit to the whole society if a person gets a flu shot. You get the benefit of the person not giving you the flu and making you sick, and you don't have to pay anything for that benefit. Doctors may have a cost as a reduced number of patients. Hospitals may suffer the same cost. Or, it could be a benefit, if the doctors offices and hospital beds are already at capacity.

As a policy maker, you may believe that free immunizations and vaccines are a public good, and you would continue or expand the system.