The issue of accessibility in web design relates to how easy, or even possible, it is for the target group of visitors to use your website. In order to provide a website that is truly usable and accessible, it is crucial to have a good understanding of your target audience. For instance, websites that will have predominantly older visitors - say, something relating to retirement - should employ larger header and body text sizes so that users will not have to struggle to read the text on the site (or go looking for their reading glasses). Similarly, a website geared at children should employ simpler language and use an inviting color scheme.
Designing with your audience in mind will help solve many crucial decisions throughout the design process. Color palettes, word choice, and complexity can all be tuned-up at different levels as dictated by the markets and audience you are trying to reach; using the proper aesthetics for your audience will build trust and goodwill amongst your users. If your company has already gone through a branding and identity exercise, these are things that you will most likely have already figured out.
The ultimate goal for most websites is to make it next-to-effortless for your users to find the information they need in an intuitive fashion. The more appealing and easy-to-use your website is, your audience and customers will enjoy using it more and will respect your brand as well; every customer interaction with your website is also an interaction with your brand. There are best practices to dictate how to make your website more accessible to a given demographic or target group, but also some thoughtfulness and testing are important to nailing a design that works well.