So I decided to refresh my Kerberos knowledge. Turned out I couldn't really describe the whole service auth process from scratch so started digging into complete explanation. Didn't manage to find in in one complete useful document, but compiled a list of great sources. The links are in order I read 'em to obtain complete and thorough knowledge enough for my daily duties.
1. Microsoft's Basics Concepts — A good place to start, nicely laid out but illustrations aren't the best in 2017.
2. ELI 5 Kerberos — Not really the ELI5-style after all, but this one if good to refresh the order of the actual user interaction with KDC and TGS.
3. Moron's Guide to Kerberos — Actually, I recommend to read this after the first link. Really helps to build the big picture.
4. Kerberos.org — the tech info you would still need to know after all you read.
Nothing special, really, and the articles are easily googled in a minute but anyway, helped me a lot.