First delete the section(s) in your data source, whether you are using a data model like Core Data or a dictionary/array.

Invoke the deleteSections:withRowAnimation: instance method of UITableView on your table view. The first parameter that you need to pass to this method is of type NSIndexSet and this object can be instantiated using the indexSetWithIndex: class method of NSIndexSet class, where the given index is an unsigned integer. Using this approach, you will be able to delete only one section at a time. If you intend to delete more than one section at a time, use the indexSetWithIndexesInRange: class method of NSIndexSet to create the index set using a range and pass that index set to the aforementioned instance method of UITableView.