Accessible design is so important, especially in this day and age, because it promotes inclusion of all types of people. When designing with accessibility in mind, you open up the doors to all kinds of people globally to interact with your designs, regardless of their language, location or ability (Accessibility, n.d.)
The web, for example should be accessible to all types of people, providing equal access and opportunity to people with diverse sets of abilities. Why is this so important? Well, for one, accessibility promotes social inclusion for people with a disability or for the elderly. Accessibility even goes so far as to provide people in rural areas and developing countries equal access to all the resources and opportunity the internet has to offer. Matter of fact, the UN Convention on the Rights of Persons with Disabilities states that access to information and communication technologies, or in other words the Web, is a basic human right (Accessibility, n.d.).
Accessible design also presents many benefits to the designer or business in question. On the web, studies show that accessible websites tend to garner improved search results, much lower maintenance costs (as good good web design practices often go hand-in-hand with accessible design practices), and higher audience reach (Accessibility, n.d.).
Let me end by sharing a quote I think sums up the importance of accessible design, in terms of the web, but that can be applied to most if not all design:
“The power of the Web is in its universality.
Access by everyone regardless of disability is an essential aspect.” – Tim Berners-Lee, W3C Director and Inventor of the World Wide Web
Accessible Design - How you can do it. 