White plays in order to strengthen the lone stone. Of course Black will expect to become stronger here too: Black at a is probably automatic unless
is played as a ko threat.
This variation is normal in contemporary pro games. Next White plays a or b, depending on the position on the upper side and the need to protect her shape.
Black can also play at
to trade the corner for a position on the upper side.
There can be a number of ways to play this variant, but this is a representative sequence, with White alive in the corner.
In recent years White has tried the immediate cross-cut at , raher than the staircase, presumably to avoid this development.
It is also possible for Black to connect solidly with (according to the advice about the staircase). Both groups then have good shape, and Black may want to make a flanking extension immediately on the left side.
With the knight's move extension, the double hane (osae) is a rare play in pro games (differing from the case of
at a). There is probably more than one reason for that: White at b can be helpful if White is looking for sabaki here; there is feeling that Black is being forced into Overconcentrated shape, too.
White's other idea is to play here for a bulge formation. Black probably takes up the challenge of a ko after
and
. The steady play of
at a is also seen: White can still provoke a ko with White at b,
,
, but this ko is a little better for Black.