The Extract function is meant to help Photoshop users with extracting elements in an image: that is, it is meant to help the Photoshop user select the elements in their images and isolate them from the background. The idea seems to be that the Extract function should make such projects as snipping a person with whispy blowing hair easy to do regardless of the background. It is useful for that to some extent. However, the tool may prove more valuable if it is looked at as something more generally helpful to improving your images and as a means rather than merely an end.
While Adobe accomplished some interesting and helpful things with the function, Extract, while useful, isn't a silver bullet for all masking needs. It can work very well and quickly in certain situations and can greatly simplify some targeted color corrections for example it doesn't necessarily make every extraction "easy." It does make some parts of selection and masking easier to do, and does it in a way that is more unified and easier to control than when using some other tools. For example, using Color Range (which makes a mask based on color) will help you make selections based on color, but won't let you limit the area that is included and refine and retouch the mask that gets created. Of course, you can limit the area by selection when using the Color Range, and you can edit the mask by using the alpha channel that gets created, but Extract tries to bring these (and other) masking functions closer together. The result hopefully being that they are easier to use.
Using Extract will take some practice and a little attention to detail to get the best results. The intent of this tutorial is to show how to use the extract tool, how to make use of its features and how to get the best results with it for the purpose of Extraction. Some possibilities for how to apply the tool and results in the Comments section hopefully show some of the extended possibility of extraction as well.