This way, no-one cuts across lanes where traffic has a green light.
In "normal" fashion, you'd have to stay on the left of your lane, and wait for the traffic coming in front of you to die down before you can cross. That puts you straight in the middle of the intersection for some time, which is dangerous.
With a hook turn, you go and wait along with the traffic coming from the east to the west. They are stopped, so they are not a danger to you. When the east-west traffic light finally turns green, you won't be crossing anyone's traffic, and you'll be already standing on the rightmost part of your new road.
They work even better with dedicated bike infrastructure as depicted in the diagram about half way through this article: https://www.vox.com/2015/8/12/9139771/protected-intersection...
https://www.youtube.com/watch?v=Yh92LirlCf8
My wife used to drive in the Melbourne CBD daily for work, but would always go around the block instead of attempting one.
This is known in the right-hand drive cycling world as a Copenhagen left, and many consider it to be bad infrastructure design.
http://www.aviewfromthecyclepath.com/2010/07/not-really-so-g...