Well I'm not acquainted with Apk tool, but I understand a bit about reverse engineering, so I went on their github page to read about it.
Essentially, an android application is packaged under the .APK extension which lets you install and run the application on your phone.
This is akin to a software with the .exe extension on windows.
An .apk or .exe is a bunch of compiled code and ressources, this means that in this form, the code is mostly a bunch of mumbo jumbo that no one can understand or make edit to.
By reverse engineering, you transform the .apk to it's initial state before compilation, the code is now organised, readable, and editable.
This allows you to understand what is going on under hood and add new code and functionnalities.
If you decide to edit the code, you can package/compile this extended application into a new .APK and enjoy additionnal features in the application.
Note that reverse engineering will not get you an exact copy of the code and file structures the original developper created, it is (in general) an approximation. Depending on the decompiler, you can lose variables names, function names...etc, but the code will work fine.
For an example
If the original developper had this function.
private String getAge(String userId) {
String age = this.users.get(userId);
return age;
}
You get the code, but it's harder to understand than if you had the original code.
So reverse engineering / decompiling is useful in some use cases, but not always a miracle.
I believe it was this tool that I used after I bought an app to them install the app on a phone that didn't have Google Play. I turned an installed app into an APK and copied it to another phone.