Almost all Android manufacturers tend to modify the stock Camera app provided by Google to add new features. One thing that most of them added was the ability to combine multiple shots into one picture showing motion, like the image above. The stock Android camera doesn't have this, or most other extra features added by the likes of HTC, Sony or Samsung.
Even Google added this feature recently to the growing list of Auto Awesome images Google+ can create. So if you take a series of shots with your phone, you can hope that when you get home, Google+ will have automatically made a motion image for you.
Sony's Motion Shot app provided this feature, but it was exclusive to the new Xperia Z1...until now. XDA-Developers member xperiaz2 just released a modified version of the app that promises to work on all Xperia devices running Android 4.0 or newer. There are also people in the forum thread saying it works on other, non-Sony devices, like the Galaxy S4 or Nexus 4.
As with all unofficial apps, please use caution in installing it. If you are uncomfortable using unofficial apps from forum threads (which you should be), then we'd suggest passing on this one. But if you are okay with the risks and trust the source, proceed. You will need to download the APK file from the XDA thread and install it on your device. Note that you will need to go into Settings, Security, and check the box next to "Unknown Sources" to be able to install this. You should probably go back and uncheck that box once you're done.
The developer only claims this will work on Xperia devices, but since many other users are reporting success, it might be worth a try on your device. If this is a feature you have been waiting for, or if you just want to take control over your motion shots yourself instead of waiting for Google+ to (hopefully) make one automatically, this looks like it could be a good app for you.
Motion photography can be really cool if done right, so if you do decide to give it a try, be sure to let us know how it works and maybe even share some of your results!