If Abraham is the father of Jewish people, who is the father of Abraham? That's right, today you're gonna learn some Jewish mythology, dear readers!
His name was Terah, and he is mentioned in the Bible, be it in passing. We know his father was Nahor, and that he fathered Abraham (then Abram) past the age of 70. (Oh, the potency of those aged ancient men!) That's pretty much it.
The rabbis tell a longer story. According to Jewish tradition, Terah ran a store that sold home-made idols. Abram was not exactly a fan, smashing his father's creations. (We're not sure if that was a sign of future monotheism or just teenage rebellion.) In any case, Terah got pissed off and brought Abram in front of King Nimrod. The king's response was to throw the kid into the furnace. (Oh, the ancient judicial system!)
Abram somehow escaped, and then Terah, for whatever reason, repented. (You can imagine that the first meeting after the furnace incident didn't go too well.) He then proceeded to lead the family on that mysterious journey to Canaan, but died on the trip. Abram took over, met G-d, renamed himself Abraham, etc. You know the rest: Jews!
(As an aside, the furnace incident kinda puts a new perspective on the whole Isaac sacrifice, doesn't it? You would think that someone who lived through that would be a little nicer to his own son? Or perhaps not. We're not psychiatrists.)
Oh! And Terah was also the father of Sarah, Abraham's wife. Don't you love our Jewish mythology, dear readers?