The code fragment takes the URL path, splits it up at each / character and then adds each fragment to the css class list. That gets added to the outermost div in Layout.cshtml where it does
var tag = Tag(Model, "div")
So a page with an url like /product/software-product/orchard-cms would become
<div class="product software-product orchard-cms">
Now you can use CSS classes to do anything you like that's specific to a page on specific elements on the page, e.g. put this in Site.css for your theme to style just the pages that are under the path .../software-product/...:
background: url(../Content/Images/productbanner.png) top right no-repeat;
You could modify the code to add more classes if you wanted, for example: one where you replace all the / characters in the path with - characters so you can have a class that's specific to one page, or perhaps add -last and -first to the first and last
elements of the path too so you can be sure you aren't referring to some other part of the path in cases where it's ambiguous.