Dr. Carol Marcus is a fictional female Human in the Star Trek - The Original Series television series who was portrayed on screen by Alice Eve. Dr Carol Marcus is the mother of Kirks' son David who makes her first appearance in the new timeline in Star Trek, Into Darkness. In the original timeline, David is bought up by Dr. Carol Marcus in a single parent household.
Her appearance in the second film includes a rather gratuitous underwear scene which we suspect is vital to the storyline (the previous line was written before the film came out). I'm sure they'll not be too many complaining about that... Whether it is unnecessary or not, you decide...