There are a lot of ways to continue after . The move is not very often played. It makes more sense to play a simple nobi, instead of this hane.
After black's hane white should make good shape with of course.
Now is a clever move which keeps black from being closed in, inside the corner. But on top of that it makes influence, which makes possible.
is the key-move in this sequence. But the exchange of for is clever, because it creates more aji than directly playing .
If white chooses to play on the left side instead, then black should create a solid connection. Later on black can still get the corner.
It is also possible to build influence towards the other side. The kosumi is flexible.