A meaningful exercise that requires using a destructor
Create an object that creates a new file and writes in to it over several method invocations (not just one). Assure that the object has been deleted before continuing (Make the object go out of scope on the stack or delete a reference and let the reference go out of scope.) You need to assure that he file was closed. The destructor is the proper place to assure that this happens. 

To verify that it works correctly, create a different object that reads from the file. If the first object didn't properly close the file this won't be possible. 

In some, at least, operating systems you don't even need the second part. The file won't appear in the file system if it was never closed.

The reason for wanting the file written over several invocations of some method(s) is that, if it is just one, an explicit close would be natural in that method. The reason for wanting any references to go out of scope is to assure you that the first object has no effect on the second. 



Edited for clarification.