This video by Chris from Spoon Graphics does a good job of going over many of the options available inside Photoshop for cutting things out. The most common use is to cut out the subject from the background, to place it on a different image or background – as in when making composite images.
Watch as he goes over the options for cutting things out:
Quick and dirty selection tools and methods:
Eraser tool (not the best choice, this is shown in the video)