Edward Masen, Sr was Edward's deceased biological father.
Edward was a very successful lawyer living in Chicago and was moderately rich, but also emotionally distant from his son. In the series, he is only mentioned by Carlisle in New Moon. He was married to Elizabeth Masen, Edward's biological mother, and he died of the Spanish influenza in 1918 before his wife also died and his son was changed into a vampire by Carlisle.
Edward Sr has no physical role in the books or the films.