While running a test case, you may find a discrepancy in the test case details or you may simply like to update the test case; for this there is an option to edit the test case on the test case view pane.
After saving the testcase and refreshing the page in web browser. You will get an option to update the version of testcase to be executed.
Note:
You can edit a test case only if your role in the project allows you to do so
Edit option will be available for a test case irrespective of its current execution status
Once a test case has been executed in a test plan, the option to see the details of newer version of test case will not be shown on test case run page, as you will be shown the version of test case that was executed.