Stage3D is a low level API. Such are common in graphics, as they are the best ways to talk to hardware, putting the least between programmers and hardware so the code they write has the best performance.
But many developers don’t want to code at a low level. They just want to put a few images on screen, or a few lines of test, or some 3D models. For these developers there are high level APIs and environments, and these are very common, as anyone can create them for any platform.
Typically they are created for a purpose, such as for 2D drawing, 3D drawing or text rendering. They also often abstract away differences between low level platforms, i.e. offer a single API for multiple platforms.
Starling is a high level API, one of many for Stage3D. Its main purpose is for creating 2D apps, rather than 3D or text (though it supports both). It does not need to abstract differences between platforms as Stage3D does that, though it does offer a similar API to the classic Flash API. And others have ported it to other platforms, such as Haxe.