DataAdapter are indeed work as an interface between data source and the data set as you have denoted. There are several options you can perform on a data source. These SCRUD (Search, Create, Retrieve, Update, Delete) functions are performed through SQL statements. As you are going to preforms these operations on data through the DataAdapter you should specify the way to performs these tasks, because all of the depend on the structure of the data source you are trying to access.
Spesifically talking about the example, it defines the SQL commands. Search command works via country and city, when you need to create a new Customer record, you have to provide CustomerId and Company name etc.
You define those commands once, and then use the same command for all operations on the same data source. This answer also gives a spesfici example on how to use DataAdapter's Update command.