What does the"wait_window" method do?

Like the documentation states, it waits until the given window is destroyed. It is mostly used for modal popups, though it doesn't itself make a window modal. The call to the function simply doesn't return until the target window is destroyed To make a modal window you have to do a grab as well.

The most common use is to create an instance of Toplevel, populate that window with widgets, then wait for the window to be dismissed before doing some other action. While it is waiting, tkinter is able to continue to process events as normal.

For instance, you can disable (or defer creation of) the main GUI, pop up a "terms of service" notice, and wait for the user to acknowledge the terms of service, copyright, license, etc. Once the window is destroyed you can then finish initialization, or enable some widgets, etc.

The standard file dialog is a perfect example: you pop up the dialog, then your code waits for the user to pick a file, then it uses the filename that was returned. Internally, the implementation of the dialog uses wait_window so that it doesn't return until the dialog is dismissed.