The one-paragraph explanation
An APK is the app itself. An XAPK is the app plus its luggage: extra data files bundled into one package. Lovely Craft APK ships as an XAPK because the 44 MB download carries game data alongside the code. Same game, slightly different suitcase.
Why developers use XAPK
Big games split code from assets so updates can replace one without re-downloading the other. For players the practical difference is tiny: you need an installer app that understands the format. The Play Store handles this invisibly; when you sideload from a source like the Lovely Craft APK download page, you handle it with one free app.
How to install an XAPK
Install any well-reviewed XAPK installer from the Play Store, download the the game XAPK, and open the file through the installer. Allow unknown sources when asked, tap Install, done. The full install walkthrough shows each screen.
What not to do
Do not rename the .xapk to .apk: the system installer still cannot read the bundle and you will get a parse error. Do not unzip it by hand either; the installer places each part where the game expects it. One app, one tap, and the Lovely Craft APK homepage build is ready to play.