First of all, every hour some creatures will be summoned at Knight's Arena, where you can kill Trolls, Frost Dragons, Dragons, Scarabs etc.
If you talk to King Tibianus during this mini world change, you'll receive the achievement "Loyal Subject"
Around Thais, some things will change: All town will be decorated, some festive tables will be found in the castle, and every Sunday you'll be able to enter the Museum for free.
The NPC Aruda will steal 10gps instead of 5.
If you say some bad word to the King, he'll send you to prison, where you will be until the next invasion is summoned at knight's arena. You can't logout while in prison.
Here: https://www.tibiawiki.com.br/wiki/Mini_World_Changes#Kingsday you can see all creatures that can be summoned and photos of the decoration at depot and tables.