This is the 7868th most frequent Polish word.
mikołaju
It means "to Nicholas" or "Santa Claus" (vocative case).
Here, 'Mikołaju' refers to addressing Santa Claus in a direct and polite manner, using the vocative case to convey the intention of speaking to or about someone directly.
Drogi Mikołaju, co przyniesiesz nam na Gwiazdkę w tym roku?
Dear Santa, what will you bring us for Christmas this year?
In this case, 'Mikołaju' is used to directly address Santa Claus, again employing the vocative case as this is a direct address within a sentence.
Nie zapomnij, Mikołaju, że dzieci czekają na Ciebie.
Don’t forget, Santa, the children are waiting for you.
The word 'Mikołaju' is once more utilized in the vocative case, expressing gratitude and directly addressing Santa Claus in a polite and formal way.