What is the Slicing option in Illustrator and Photoshop Used for? Doesn't the Guides option provide such functionality?
Slicing is the technique in Photoshop and Illustrator that allows you to divide the image in small parts to use it later on a website, interface etc.
This is the only purpose of the slice tool: you can design an interface in Photoshop and chop it in small parts, dividing it in buttons, images, menus and background, and then export it as separated images. When developing web sites, it could also generate (mostly poor) HTML for you.
Wikipedia has an article on this: Slicing (interface design)
You can generate slices from guides. I think that's the only relation they hold.
See this question: What is the standard method of slicing a photoshop document?, specifically Lauren's answer.
Expanding on Thiago Silveira's answer:
I tend to use Slicing a lot when designing HTML emails. The generated HTML is so primitive (i.e. uses tables for layout) that the HTML emails are compatible even with Outlook 2007 & 2010 (which uses a poor standard HTML rendering engine).
Slicing is used with Save For Web & Devices. When you hit save from this screen you can see a drop down menu on the bottom of Finder (or Windows Explorer if you are so inclined) to select HTML Only, HTML & Images or Images Only: