CSS Specificity is the process by which the browser decides which CSS values are most relevant to an element, and therefore will be applied to it.
Contrast Ratios are the difference between the minimum brightness and the maximum brightness or black and white.
You have to meet the contrast ratio because it is crucial for your website to meet a certain level for people who may have a certain level of color blindness or something that impairs the way they will see it.
All standards are reviewed for accessibility support by the Accessible Platform Architectures, or (APA) for short, Working Group.
In summary for specificity it is almost all done by the browser so you don't even have to worry about it. Contrast ratios are something you have to worry about though. If your website does not meet the standards or get a rating of AA or AAA it may be flagged as not fully accessible for all users. In which case you would have to make adjustments to your colors and make them more up to standards. Then your site will be tested to then determine if it is up to standards and after which, if your site passes, will be given your new rating and labeled as more accessible for users.