This is the 3333rd most frequent Polish word.
urodzin
"Urodzin" is the genitive plural form of "urodziny," meaning "birthday."
The word 'urodziny' means 'birthday' and here it is presented as a noun in nominative plural, used to denote the specific day of birth celebration.
Mam dzisiaj urodziny.
It is my birthday today.
Here 'urodziny' is in the accusative plural case, portraying the event for which the gift was received.
Otrzymałem prezent na urodziny.
I received a gift for my birthday.
In this sentence, 'urodziny' again signifies the birthday occasion, emphasizing the first anniversary of her birth, with appropriate grammar for contextual meaning.