Emily's father is the guy with the gigantic horsewhip. He's only referred to as "Emily's father." Faulkner himself didn't approve of the man at all. In an interview, Faulkner expounds on this character:
In this case there was the young girl with a young girl's normal aspirations to find love and then a husband and a family, who was brow-beaten and kept down by her father, a selfish man who didn't want her to leave home because he wanted a housekeeper, and it was a natural instinct of – repressed which – you can't repress it – you can mash it down but it comes up somewhere else and very likely in a tragic form, and that was simply another manifestation of man's injustice to man, of the poor tragic human being struggling with its own heart, with others, with its environment, for the simple things which all human beings want. In that case it was a young girl that just wanted to be loved and to love and to have a husband and a family. (source)
That description is pretty straightforward. The story is meant to show a very selfish man in a very selfish society. He's kind of a one-note fellow, and that note is Me, me, me, me, me!