First, you could learn some fun facts. For instance, my grandmother Gertrude Francis Stenglein was actually named Gertrudt Francisca Stenglein on her birth certificate. Very German! Since her parents had only arrived in the U.S. in 1891 and still spoke German, this isn't a surprise but is still fun to see.
Most importantly, you may learn more about the child's parents. My great-aunt Laura Caroline Huber was born in 1906 in Reserve Township, Pennsylvania. It showed her father's occupation of engineer and that her parents were living at 38 Luty Avenue in Reserve. Her birth certificate also gave me a clue that I hope helps me track down more information on my great-grandmother.
Laura's mother, Alice Laubersheimer Huber, is a bit of a mystery to me since I've been unable to find out where she was born nor verify the names of her parents as passed along in family oral history. Laura's handwritten birth certificate only gave the birthplaces of her parents as "American" and "German." However, the typed version shows that Alice was born in "Strassburg, Alssaice-Lorraine."
I believe this is Strasbourg, France, which is near the border of Germany. This was very exciting to learn since French records are online and I've had a lot of success with them in the past. I browsed the records of the Bas-Rhin Archives but haven't had any luck finding Alice's birth. I'm hoping to perhaps find her in a nearby town.
Anyway, although my post doesn't have a happy ending, hopefully you can see how birth certificates could provide a clue to help you advance your family research. Take a look and find out if you can learn any interesting things about your relatives.