Accessibility is all about ensuring that everyone has access to your product. Basically, it doesn't. Usability is all about ensuring that you build a product that is effective, efficient and is easy to learn and use for the target users. If you design a product with very poor usability, then your users cannot 'access' the functionality and use it. When you design, you take into account the different tool sets that users have - for example, you design a site to work in as many browsers as possible, as some users will have older versions.
Accessibility is exactly the same issue.
Not all of your users are accessing your product with the same mental and physical 'tool sets', and just as with software tool sets, you need to design accordingly. The problems encountered depend on the special needs of the user and the design of the product, but generally these can range from making it annoying to use the product right the way up to making it impossible to use the product. The 'Bobby' test - Cast.org offer a tool called Bobby that will help to identify accessibility issues in your site. The UsableNet test - UsableNet offer a similar tool that tests for accessibility and basic usability guidelines online. The 'images off' test - If you want to see how a blind person using assistive technologies would experience your site, then turn off images in your browser and load your page.