Here's the basic rundown:
Haxe is a programming language, similar to ActionScript.
OpenFL is an implementation of the standard library from Flash, with classes like Sprite, Bitmap, TextField, URLRequest, Event, Sound, etc. You can think of OpenFL being like Flash Player and AIR.
When you create an app with OpenFL, you can build native apps for Windows, macOS, Android, and iOS (and some others), like AIR. You can also use OpenFL to target web browsers, like Flash Player (except your app will run on JS instead of a plugin). Basically, OpenFL is both Flash Player and AIR rolled into one.