Android P seems to be laying the groundwork to ensure apps reach a minimum requirement level when it comes to general performance and security, compared to previous versions of Android. Along with a fairly clear suggestion Android apps that are not up-to-date enough will likely be forbidden from running on devices utilizing Android P, and newer.
This information comes from a new MIN_SUPPORTED_TARGET_SDK_INT reference found within the developer preview of Android P by Reddit user thecodingdude. A listing on the Android developers page for the same class reference further expands on this point by stating that apps which do not target this minimum SDK requirement "will fail to install and run." Largely suggesting that apps targeting a younger version of Android will not be compatible with Android P. This is slightly different to an announcement which came through in December, 2017, where Google – via its developer blog – first explained more current API targeting would be required. While that announcement did focus more on how new of an API developers should be aiming toward, it also did make it clear "future Android versions will also restrict apps that don't target a recent API level." Therefore the wording seems to be much stronger now with the use of "restricting" having been strengthened to 'fail to run.'
As for the specifics, the same redditor notes that the class reference in this case relates to SDK (or API) 17. In other words, Android 4.2 (Jelly Bean). Therefore, this is not a case of where apps will need to be minimally compatible with an extremely new version of Android. While that is the goal according to the previous announcement, developers will still be able to offer support for most legacy versions of Android. To put this into perspective, the Android distribution figures (as of Feb. 2018) show only 2.4-percent of devices run a version of Android earlier than 4.2. It is also worth pointing out it is possible this particular caveat will be specific to apps that are downloaded through the Google Play Store. As it would stand to reason that developers are able to run any Android version of an app on the latest version of Android – for testing purposes, if nothing else. Likewise, this minimum API target is also a moving goalpost as the documentation relating to this does specify as newer versions of Android are released, the minimum API level will be increased to the next minimum value.