The Web Accessibility Initiative Accessible Rich Internet Applications Suite (WAI-ARIA) are a special list of recommendations by the W3C designed to help developers of Rich Internet Applications maintain accessibility.
Most websites do not rely heavily on ARIA-style components, but many have at least one ARIA-style component (a drop-down menu). If you are coding your website by hand or using an open-source framework (like Drupal, Wordpress or Joomla), you may need to study ARIA more than if you are using a pre-canned web hosting solution.
What is a Rich Internet Application? It is a broad term used to describe "desktop-like" functionality in a website. Draggable elements, dynamically-changing content (such as a slideshow), and drop-down style menus are examples of Rich elements. These Rich elements generally rely on either Asynchronous Javascript (AJAX) or another method of dynamic manipulation of the Document Object Model (DOM).
Dynamic manipulation of the DOM makes accessibility challenging. Screen readers and keyboard navigation are difficult when the HTML is manipulated at run-time, especially if a mouse is used to trigger this manipulation.
While the ARIA specification is much more technical than the WCAG2.0aa guidelines, it is not generally necessary to understand the intricacies of the ARIA. It is most important to understand which elements of your website may be impacted by the ARIA and then to ensure that those elements are accessible. The elements to most watch out for on your website will be:
One example of how the ARIA impacts accessibility can be easily seen in ARIA Section 5, Defining Keyboard Navigation. If you glance through Section 5, you can see that menu and other section navigation must be completable via Keyboard navigation. The ARIA style recommendations show how to technically accomplish this navigation accessibility.
This video describes a brief overview of the ARIA guidelines and how to ensure proper implementation. Again, if you are using a hosted solution and suspect that one or more of your Rich Elements is not accessible, you should contact your hosting company regarding the concern and discuss remediation.
Here's a Google Developer video on using some Chrome tools to test accessibility. At about 3:40seconds into the video, there is a discussion regarding online accessibility tools and how their results may not be completely accurate regarding a website's true accessibility. A ton of great tools and tips are listed in this video.