By making Edge apps available on non-Windows operating systems, Microsoft is hoping to do more than give Windows 10 users who use Edge a more convenient way to sync their bookmarks, tabs, etc., across devices.
Microsoft also is doing this to improve its "Continue on PC" feature that it's been touting for Windows 10. With "Continue on PC," users will be able to share a web site, app, photo, and other information from their phones to their Windows 10 PCs in a faster and more seamless way. Microsoft is looking to Continue on PC to help keep Windows PCs relevant in a world where more and more computing is done on mobile devices.
Instead of using the underlying Microsoft EdgeHTML rendering engine, the iOS Edge app uses Webkit like Apple does, and the Android Edge app uses the Chromium Blink engine.