Every web designer tries to make their sites as usable, understandable, and beautiful as possible. Web accessibility is the practice of ensuring that you site is equally usable and understandable for all people, including the disabled. It may not be obvious, but many of the web accessibility best practices will help you create a a site that is actually better for all users, not just those people we generally think of as disabled.
Consider a very common disability that doesn't usually jump to mind when you say "disabled": color blindness. About 7% of men and .4% of women in the united states have some form of color blindness. Because of this, it is not a great idea to use color alone to signal some special functionality on a web page. But "color sighted" users shouldn't have a problem, right? Well, not every monitor is properly calibrated and on some low cost LCD monitors your users may have trouble distinguishing colors that are plainly different on your screen. Even high contrast colors may not show up in black and white printouts of your site.
<select name="xxx" onchange="this.form.submit();">
Another web accessibility best practice is providing "Alt" tags for images. The Alt tag provides a text description of the image. Originally this was used so that screen readers could describe the image to a blind user. Now these Alt tags provide valuable meta information to search engines trying to connect users with your content. Doing this consistently can push your site higher in Google's search results.
The recent push towards mobile web sites ties in well with the accessibility concept also. What might work fine on a 21" monitor with a good mouse does not usually work on a 4 inch smart phone screen. Web accessibility recommends using large "click targets" to support users with impaired motor skills. But keep in mind that large targets will help all your users when they are tying to get something done on your web site using a phone or tablet. Especially if they have to poke at the tiny screen with their finger on a bouncing commuter train.
If you are interested in learning more about Web Accessibility guidelines at the W3C's Web Accessibility Initiative site.