White 11 makes a first eye, a and b being miai. White 13 threatens to kill the corner in a capturing race: see variation [2]. Hence Black 14 connects. White 15 makes the second eye. If she omits it, Black at c or 15 destroys the second eye.
[1]
If Black 8 at here, White wins the capturing race. Losing four moves with a to d, she still has 7 liberties left to attack, while Black has only three to defend (he'll have to react to one).
[2]