It's a common Hindu tradition in which a priest(Pundit) makes a "Birth Card" based on the arrangements of the planets on the day you were born. It's a detailed astrology chart or script which mentions the effect of the planets on the person, usually throughout the person's lifetime. It's somewhat a combination of numerology and astrology.
Apart from that, I've never heard of the term being used before. I'm sure that anyone can get a "birth card". But it all depends on the priest. Some charge you and others don't.
I had one made, but my birth date was entered incorrectly, so it didn't apply to me. Still have to get it remade. -.-
I hope you got the answer you were looking for.