This is the 4365th most frequent Polish word.
gwiazdkę
"Gwiazdkę" means "little star" or refers to "Christmas" (as in holidays or gifts) depending on context.
Here, 'gwiazdkę' refers to Christmas, a holiday occasion, and is in the accusative case as part of the phrase indicating an action of giving or receiving related to that event.
Dostałem prezent na gwiazdkę.
I received a gift for Christmas.
In this sentence, 'gwiazdkę' is used to mean a star, referring to a decoration or element in the dessert. It is the object in the request, hence its accusative case.
Poprosiła kelnera o dodatkową gwiazdkę w deserze.
She asked the waiter for an extra star in the dessert.
The word 'gwiazdkę' refers to an astronomical star, used figuratively as a diminutive to highlight its beauty or smallness. It is in the accusative case as it is the object of the action of seeing.