1. What is the general goal of the feature?
To have a search option where all the options (under select_one) are not shown together. Only the filtered options are shown when the user starts typing something in the edit text. This would make the UI less cluttered when there are a lot of options to choose from. So basically a drop down menu with a search option.
2. What are some example use cases for this feature?
An example could be the Google Home Page. It just has the search box in the middle and when user starts typing something, it gives matching suggestions.
Here are screenshots of an offline dictionary application as another example:
In ODK Collect v1.28 Beta 1, the minimal appearance can combine with any other select appearance including autocomplete/search (those two are the same). The interface is very similar to @zoey's example but the choices are shown in a full screen dialog rather than a dropdown.