The purpose behind app indexing and deep links is to enable someone who searches on their smartphone to be able to click from the search results directly into the relevant content within an app they have on their phone.
So if you search for ice cream stores in NYC, if an app comes up, it should link you directly to the app content with that information. When it doesn't, that it is a bad user experience and technically, it goes against the app indexing guidelines.
Google has been sending some webmasters notices when these things happen. The message reads:
Fix app deep links to [URL HERE] that don’t match the content of the web pagesDear webmaster of URL,
When indexing the deep links to your app, we detected that the content of # app pages doesn’t match the content of the corresponding web page. This is a bad experience for your users because they won’t find what they were looking for on your app page. We won’t show deep links for these app pages in our smartphone search results. This is an important issue that needs your immediate attention.
Sunny K. Ujjawal recently spotted this message and posted it on Google+ but this has been floating around for at least six months now.
Here is a picture:
This seems to be a mix between a manual action and a debug notification from Google.
Forum discussion at Google+.
Update: John Mueller from Google said on Google+ that this is not a manual action email, but rather a technical help email. He said, "This is really just a technical issue & a notice to encourage the owner to fix it."