Interstitials are pages or parts of pages displayed on web sites before showing the actual content. The intent is to block the user from seeing the content before making a decision (click an ad, subscribe to a mailing list, download an app). They have been commonly used for displaying ads but an huge number of sites are using them for making the user to download an app.
There is a recent study of using app interstitials by Google (on their very own Google+, a now long dead social network). The conclusion of the study is negative: app interstitial suck. I was one of the unfortunate users who tried to use it on a mobile phone. Attempt to view a Google+ page on my Android was interrupted by a prompt to install the Google+ app. I decided to not install the app but also found no way past the prompt. Also, all my Google Authorship links (on a mobile-optimized site) took to a Google+ page that also asked to install the app. Thankfully, authorship is now dead too.
Google has now a Mobile SEO Guide and it includes "Avoid interstitials" as a best practice. Furthermore, Google is considering making interstitials a negative ranking factor. This includes both ad and app interstitials.
An alternative solution to app interstitial is a small banner with a link taking to the app download page/appstore (if the site needs an app at all!). Let's follow the great quote from Google:
Let's remove friction and make the mobile web more useful and usable!