Mac Kung Fu:

Renting a title larger than the remaining capacity on your device forces iOS to use a hitherto undisclosed clean-up routine, thereby freeing-up space. Even if the download is way too big, it’ll still try to free-up space.

[I’m rewriting this post, with feedback from a number of people]

This technique has been around for quite some time. From this OSXDaily post [H/T Mark G]:

You may have noticed that some iOS apps will turn dark as if they’re being launched and simultaneously rename themselves as “Cleaning…”, seemingly out of the blue and at random. This is demonstrated happening with the attached iPhone screenshot, showing the Instagram app going through the process. So the big question for many users is, what’s going on here and why does that iPhone or iPad app say it’s cleaning?

And:

In short, when an iOS app name says “Cleaning”, it means that the operating system is going through and clearing out caches and temporary files associated with the app in question.

The post goes into detail, but bottom line, when your iOS device is low on memory, it will look to reclaim temporarily used memory, asking each app to return what it can.