What is the .android_secure Folder? On my currently working Android 4.4 phone, much of my apps and data is on a MicroSDHC card and I am trying to find what to preserve and port to a new phone. As I am trying to move from an old phone to a new one and had not anticipating significant changes in behavior, I am rather confused on how to proceed and am entirely unprepared.

When reading the MicroSDHC card outside of the phone via a dedicated card reader there is a folder called .android_secure with 18 files all with .asec extension. What are those files? And can they be used somehow to help migrate to a new Android 7.0 phone?

Note that when mounting the phone, all the folders in the MicroSDHC card appear except for that one, so you have to read the card externally to see it.

This is about the concept of the folder which you can only figure out that it is for applications if you know already the answer.
android_secure folder contains those apps which you have moved to external SD. Files inside them would have .asec extension
Android 6.0 upwards don't allow you to move apps to external SD as you have been doing. They use adoptable-storage wherein the external SD card and internal storage are merged to create a bigger storage. You can read more in adoptable-storage tag wiki. This folder is of no use to you in migrating , since the concept is different ( best is to restore all apps to internal storage before attempting backup )
Coming to the migration of apps and data,


If your device is not rooted, it is not easy or guaranteed to work since you are jumping across two versions ( this could be a separate question )
If your device is rooted , titanium-backup or nandroid backup would help