Who exactly was Hagar?
Rashi and Targum Yonasan: She was the daughter of Par'oh, 1 King of Egypt, who, when (after taking Sarah as a wife - Targum Yonasan) he saw the miracles that Avraham experienced, came to the conclusion that it would be preferable for his daughter to be a maidservant in Avraham's house than a mistress anywhere else.
Targum Yonasan (in 16:5): Par'oh himself was the son of Nimrod who threw Avran into the furnace.
QUESTIONS ON RASHI
Rashi writes: "[Hagar] was Pharaoh's daughter." What is the source for this in the verse?
Gur Aryeh: Sarah must have had numerous maidservants, and the verse could have stated, "And she took her maidservant, Hagar the Egyptian." Rather, the verse begins, "And she had an Egyptian maidservant," to emphasize that to others, Hagar would not be [deemed] a maidservant [for she was born a princess], rather only to Sarah.