After , White can't play at a because of shortage of liberties.
If White plays at b, Black can later play at a. White can then capture Black's stones, but that leaves her with a three in a row shape.
See also rectangular six in the corner.
What if White plays somewhere else?
If White answers with here, Black plays . White would like to play at as well, if Black plays at a or b. Why?
So, after and in the Variation diagram, we have a bulky five shape, with one point already occupied by Black. However, the vital point marked with a square has not been played yet. That is why Black plays at next. (And that is why White trying to live with in the first diagram seems like a good idea - but fails as well.)
Try to memorize the bulky five shape. It occurs over and over again.