Nameday

Within the fantasy world of Game of Thrones, a "nameday is the equivalent of a "birthday" in the culture of Westeros.

In Westeros, babies are named the same day they are born. Therefore, a "nameday" is functionally the same thing as a "birthday", as both terms indicate the day a person was born on. The only slight difference is that in Westeros, the act of naming is what is counted, instead of the birth itself. People receive presents from friends and family on their nameday.

In the Books
People in Westeros count their age by each annual "nameday", but this is functionally equivalent to a real-life "birthday" because babies in the Seven Kingdoms are named the same day they are born, hence the phrase "naked as my nameday". That is, it is not like the real-life Jewish brit milah naming ceremony for male babies, which takes place eight days after birth. A "nameday" is equivalent to a "birthday", its just a quirk of the characters' culture.

The only exception to this is north of the Wall, where the wildings live in such a harsh and unforgiving environment that infant mortality is quite high. Therefore, the wildings only name their children when they survive to two years old.