Edward Masen, Sr was Edward's deceased biological father.
Edward was born in the late 19th century and grew to become a very successful lawyer living in Chicago. He married a woman named Elizabeth and fathered a son, Edward, Jr. His job made the family moderately wealthy, and his son was given proper education. However, Edward was also physically and emotionally distant from his son.
Edward died of the first wave of the Spanish influenza in 1918. His wife later died in the second wave and his son was changed into a vampire by Carlisle Cullen. Though not biologically related, his son shared a father-son relationship in a way he never related to his real father. In the series, he is only mentioned by Carlisle in New Moon.
Edward, Sr has no physical role in the books or the films.