So JDBC queries return ResultSet objects. But your application has Domain objects like Order or Item. You need to convert the ResultSet into a Domain object. This normally tedious pain in the arse work, that is error proned, and in different queries might have duplicate code.
By using a RowMapper you can centralize that code in one class.
So when you run a Query that returns rows into a ResultSet and you pass in a RowMapper to the JdbcTemplate, then the template will do the work of looping through the resultset and passing it row by row to the mapRow method. The return of the mapRow will be an Object of the type that you convert the row to. In the mapRow method you write the code like
Order order = new Order();
I forget the exact api method call on result set to get the field value of a date, but that is the general idea.