A static web page is a document (a file) which contains all of the information necessary to display the page content (though it may draw images and styles from other places). These are typically named [something].html.
A dynamic web page pulls information from a database, and so may serve many different purposes. For example a dynamic product page can be used to display different products depending on what parameters are given.
Whether or not you edit the website using a content management system, that system could potentially produce static or dynamic pages
Some people favour static pages for speed and for google spidering.
Speed can be an issue if the server is being pushed to the limit, but web servers are still able to cache dynamic pages in many situations, so static pages may not have that much of an 'edge'.
Google likes web pages with names that make sense, so toaster.html rather than product.php?r=9219192. However, tools like mod_rewrite and ISAPIRewrite can turn static-looking web addresses into calls to dynamic pages, so you really don't need static pages to impress search engines.
The big disadvantage of static pages is that they can never do clever things like saying 'welcome back, [name]', or displaying your current basket total in the corner.
We always recommend dynamic pages, unless there is a specific, proven speed issue and extra hardware is prohibitively expensive.