Blocks are used to build the display. At first they can be confusing, because it's not always clear which block is used where, but they allow you to quickly and easily change the entire layout of the site. This is where all layout changes are made; there are no HTML template files to modify. (The html/ directory in the Scoop package contains the site's static files, such as its images and robots.txt.)
Boxes, on the other hand, are bits of perl code that run every time they appear on a page. They range from very simple (the main_menu box which checks a few permissions and displays appropriate menu items) to very complex (the payment processing boxes used to handle ad and subscription payment and activation). Boxes have full access to all of Scoop's data and functions, as well as the normal Perl ability to call external programs and capture their output for parsing (the fortune_box is an example of this; it calls the unix program 'fortune' and displays the quote returned). There are a number of useful boxes included with Scoop, and quite a number of other boxes available on the Scoop Box Exchange (B).
Some of kuro5hin's custom boxes are available on the Scoop Box Exchange (B). Others aren't. The SBE is the first place to look for boxes that aren't included with Scoop.