In simple words Accessibility testing is a type of testing to make sure that your site can be accessed and used by everyone including people with disabilities. For this purpose all such sites in the United States needs to follow the "Web-based Intranet and Internet Information and Applications (1194.22)" of section 508.
Another guide to making a site accessible is to follow the "Web Content Accessibility Guidelines"(WCAG) by W3C. WCAG 1.0 was published in 1999, WCAG 2.0 is the latest and it was published on 2008.
Before starting any accessibility testing my advice to you is to READ ALL THE STANDARDS THOROUGHLY. Believe me its worth it specially if this is the first time you are doing Accessibility testing. Another advice is when ever you come across a good site or resource make sure you bookmark it so that it can be accessed easily later on. (I recommend using Google Bookmarks).
Let me now share with you some of the useful resources I came across so that it will make life easy for you when you get to testing your site. If you do find this post useful please leave a comment.
Standards and Guidelines
Web-based Intranet and Internet Information and Applications (1194.22) - Section 508
Section 508 Standards Guide
Section 508 Standards Guide
Techniques
Checklists
WebAIM's WCAG 2.0 Checklist
HTML 508 Checklist - HHS.gov
Online Accessibility Checkers
AChecker
WAVE
TAW Online
TAW3 Standalone
Deque
Functional Accessibility Evaluator
CynthiaSays
HERA
UITest.com
Online Color Contrast Checkers
Accessibility Color Wheel
VISCheck
HTML 508 Checklist - HHS.gov
Online Accessibility Checkers
AChecker
WAVE
TAW Online
TAW3 Standalone
Deque
Functional Accessibility Evaluator
CynthiaSays
HERA
UITest.com
Online Color Contrast Checkers
Accessibility Color Wheel
VISCheck
Toolbars and Addons
Other Useful sites
Screen Readers
Hope you find this useful. Please do share your experience with the tools you have used so that others may benefit.
Happy Testing!