A run-time environment is a stand-alone software (a.k.a plug-in) that displays a non-standard file type in a browser. For example, browsers can't display PDFs without a PDF viewer plug-in). For decades Flash was the standard for animation on the web. But browsers couldn't display its .swf file-type without the FlashPlayer.
RTEs add capabilities beyond those of a browser, and therefore have been prohibited from iOS devices. While Flash received the bulk of attention when Apple refused to allow RTEs on iPhones, all run-times —except their own QuickTime— were banned, since they could bypass Apple's AppStore (The notion that RTEs hog memory or are more prone to bugs was a red herring; Apple didn't want to miss out on AppStore revenue).
Examples of popular RTEs include:
* no longer under development