Version 4.0 of the Android mode introduces many changes and updates. Most importantly, this version of the mode supports live wallpapers, watch faces, and VR apps.
In order to install your sketches as regular apps or live wallapers, you need a device running Android 4.2 or higher. To install VR apps, you need at least Android 4.4. And to run watch faces, you need a watch with Android Wear 2.0 or newer.
If you have sketches that you created with version 3.x of the Android mode, you will need to manually delete the AndroidManifest.xml file in the sketch folder, so the mode will create a new compatible manifest. Remember to set the permissions requried by your app again using the permission selector in the PDE.
The Android mode now uses Gradle as its build system, after ant was deprecated in the Android SDK. When running your sketches from Processing, besides seeing different messages in the console when building the code, you should not notice any difference. However, this has implications when exporting your project. Before, the export was an ant project you could import into Eclipse with the Android Development Tools (ADT) plugin. ADT is no longer supported by Google, with Android Studio being the default development environment for Android. The export project option in the PDE will now create a Gradle project that you can build directly from the command line using the included Gradle Wrapper, or import into Android Studio.