This happens when trying to install any application from the Store on Windows Phone 8.1 WVGA 4 inch 512MB Emulator. It first asks to login with Microsoft account, create a backup and such. Then after pressing the install button for some app an error dialog appears.
Complete message from error dialog:
There is a problem completing your request. Try again later.
Inquiring minds may find this error code helpful: 80070002
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I tried following solutions from this thread, which is enabling Administrator account, logging in (so that C:\Users\Administrator folder appears) and restarting Emulator. Unfortunately this did not help.
Check the date; time and region settings in your emulator. They need to be correct.