Because App Inventor provides access to a GPS-location sensor, you can build apps that know where you are. You can build an app to help you remember where you parked your car, an app that shows the location of your friends or colleagues at a concert or conference, or your own custom tour app of your school, workplace, or a museum.
You can write apps that use the phone features of an Android phone. You can write an app that periodically texts "missing you" to your loved ones, or an app "No Text While Driving" that responds to all texts automatically with "sorry, I'm driving and will contact you later". You can even have the app read the incoming texts aloud to you (though this might lure you into responding).
App Inventor provides a way for you to communicate with the web. If you know how to write web apps, you can use App Inventor to write Android apps that talk to your favorite web sites, such as Amazon and Twitter.