Accessibility is quite connected with usability. Can’t tell you what’s exactly the difference, but accessibility is like writing the right tags. You mostly need this for people with disabilities, people who might surf the web with the help of text readers.
Accessible web site is site with good contrast between text and background, web site where you don’t have problem fining the navigation and using it. Here breadcrumb come to help in deciding in which category are you and which subcategory.
I already mentioned screenreaders. It’s nice to be aware of what those devices actually “read” on a page. For example when there is an image, the screenreader will read the alt attribute. That’s why you always need to have one and it should be a short description of what’s the on the image. I’m not completely sure, but it’s quite possible that search engines use those attributes as well to rank your content.
<strong> vs <b> – both tags make the same visual effect, but a screenreader will not mention the <b> as bold text. Always use <strong> instead.
<em> vs <i> – em means emphasize, the case is the same as <strong vs <b> – use <em> to make a text italic.
Adding text “Link opens in a new window” is quite helpful, too. You could add it as a content or as a title on the anchor tag.
Add a site map, it will improve your site’s navigation. With one glance people will be able to understand the entire content structure. Not only that, but the Site maps are used by Google for tracking and crawling. SiteMap will push your site a few spots further in the searches.
Make the text in readable size, readable color, readable font (don’t use Times New Roman as it’s font for print media). Make the text in resizable units like em’s %, than you can avoid screen resolution problems and give a chance to your users to change the font-size.
Use li tags to create your navigation, not spans or p tags.
Flash can be fancy, but in most cases it’s confusing, impossible to work with screen readers and SEO unfriendly. It’s not worthy to make a fancy site, when people cannot find it or use it at all? There could be exceptions but take a good look at your Google Analytics before you make such an important decision as to use Flash.
Accessibility is a broad topic. Here I just covered just a super tiny introduction. Otherwise, it includes matters as how your web site looks in variate of browsers, screen resolutions, devices and how well does it look when you try to print a page.
Resources from W3C about accessibility (taken from lynda.com)