The deep web refers to all the pages which are not indexed, which means that most search engines won’t return them to you after a search. Their crawlers don’t ‘see’ these pages, making them de facto invisible to these search engines.
This means that in order to access one of these pages, you need to either know their exact address (link) or to click on another link once you get in the deep side of the web. The dark web is a layer even deeper: technically also part of the deep web (which makes it inaccessible unless you know exactly where to go), but focused on illegal activities and services. It can be pretty gruesome. Some people call it the place where humanity’s darkest side surfaces.