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Explanation: It means the date of the feast day of the saint with whom you share a name. For example, my birthday is in August but my name day is 4 November, St Charles's day.
It has been customary in Catholic countries to name children after a saint on whose feast day they are born or baptised, in which case your name day and your birthday are the same or at least close in date, but this is very far from being universal practice, either now or in historical periods. In the case of royal families there were often dynastic reasons for choosing children's names; it was not determined by the calendar of saints. Take Queen María Luisa of Parma, consort of Charles IV of Spain (I don't know whether this is the Queen María Luisa your text refers to). Her birthday was 9 December; she was born on 9 December 1751. But her "santo", her name day, was 15 March, St Louise's day.