With a wealth of data-organizational concepts in the modern Tableau environment, it is easy to overlook one or another. So had I for a long time underestimated the significance of sets. It looked to me as some rudimental idea unnecessary with calculated fields and parameters being able to cover most use cases.
The reality is there is something you could not do any other way than with sets: when you need the user to select a number of items in a table. A parameter can hold a single value, while a set will carry any number of values for you, and set actions will allow a user to add and remove these values at will.
It may be used to add some complex user interactivity to your vizzes. For example, as I did in this nutritional value calculator I built for our #dashboardweek: