This is the 6010th most frequent Polish word.
życzę
"I wish."
The word "życzę" is used to express a wish or goodwill towards someone, in this case, to wish someone a happy birthday.
Życzę Ci wszystkiego najlepszego na urodziny!
I wish you all the best for your birthday!
Here, "życzę" conveys best wishes or support for success, specifically for an upcoming exam.
Życzę Ci powodzenia na egzaminie.
I wish you good luck on your exam.
In this case, "życzę" is used reflexively to express a personal desire or aspiration.