'Unborn Pendragon' is the child that Morgan Pendragon is carrying by the end of Season 1.
The implication is that the child was conceived through an act of incest between Morgan and her younger half-brother Arthur. Arthur, was unaware that it was Morgan that he was with as she had disguised herself by taking the form of Guinevere so as to fool him. Morgan, guided by Sibyl and haunted by the words of the Lady Igraine, intended to conceive a son by Arthur so that her son her would inherit the throne that she could not. If the child is indeed Arthur's, as per Morgan's intentions, then it is the currently the only heir to the throne. However, how Morgan intends to claim the throne through her child, without revealing the nature of the child's conception, is unclear.
However, less than a week prior to her attempt to conceive a son with Arthur, Morgan (this time having taken the form of her step-mother, the Lady Igraine) spent the night with the sorcerer Merlin. Thus it is also possible that Morgan had already conceived a child with Merlin when she went to Arthur's bedchamber. If the child is Merlin's then it has no claim to the throne due to Morgan having been stripped of her name and therefore no longer being considered a member of the Pendragon line and thus having no claim to the throne herself.
It's grandparents are Uther Pendragon, Igraine Pendragon (depending on the paternity of the child Igraine is at least it's step-grandmother and possibly also it's biological grandmother) and Morgan's Mother.