The best file management app for Android users is easily an old community favorite called ES File Explorer. It has been around for several years and remains highly popular for several valid reasons.
Number one, it's available on both Google Play and the Amazon App Store, making accessible regardless of the device you have. This also lets you update that app later on via whichever app store you choose. This is an invaluable feature if your options for file management are limited.
Number two, it can install APK files to your tablet of choice, even if it is a highly restrictive Kindle tablet. This is a fantastic feature for getting free apps on your tablet if you cannot access Google Play for whatever reason. All you need to do is find the APK online, usually through the app maker, download it to your tablet and navigate to it with the app.
Number three, file management is a breeze; the interface is reminiscent of a traditional computer's file system to make it as simple to navigate as possible. If you know how to find files on your computer, you should have no problem finding files on ES File Explorer as well.