It is a “modified” APK file or application package for Android. Installing a modded APK will allow functions that are not normally available for the operating system to work.
APKs are Android’s equivalent to an iPhone’s .ipa files; they’re what makes up the installation package of your Android app. With apps like apkt, you can manually edit any APKK and upload it back onto your phone, giving tweaks where needed and perhaps adding some features or bug fixes behind the scenes so when you install them on your device, it’ll show up as the latest version of the app even though it was developed long ago. It may sound like witchcraft but with these tools (and some practice), anyone can do it.
Modification is usually done by decompiling the APK (or DEX, in Android’s case), patching what needs to be patched and recompiling the files into a new APK. This is called “cooking” an APK. The result is that you end up with a modded APK that other users can install on their device without requiring root or a custom recovery.