An AAE file contains edits made to an image using the Photos app on an iOS device. It is used to transfer non-destructive edits a user has made to .JPG images in iOS to the macOS system. AAE files can be found accompanying the images for which they contain edits.
AAE files are used by iOS 8 and later and OS X 10.10 and later. If you import pictures from an iOS device to Windows, the JPEG images will only get transferred and not the AAE files, which will cause you to lose your edits. Also, AAE files can be deleted without erasing your pictures but any edits made to them will be removed.
The AAE file is referenced by the Photos app when opening the JPG file in which it is associated. The data is saved in an XML format that can be viewed with a text editor such as TextEdit or Notepad.