Most Kalman filter tutorials open with five matrix equations. This one doesn't.
The core idea
You have a guess about where you are. You have a measurement that's also about where you are. Neither is right. The filter's job is to decide how much to trust each one.
That's it. The matrices are bookkeeping for doing that in more than one dimension at a time.
Where it goes wrong in practice
Almost every Kalman filter bug I've seen came down to one of two things: a process noise value picked by vibes, or a measurement arriving with a timestamp nobody checked.