For me, accessibility has come to mean ease of use for anyone with a disability. This includes sensory disabilities as well as mobility issues. In the game industry, this can mean having to do something as obvious as adding subtitles (something not all modern games bother to do) to having more than one type of stimulus for the player whenever anything happens.
For instance, in a menu screen the words might change colors as the player scrolls over them, giving some indication they have selected something new. But for a colorblind person, this wouldn’t be as distinguishable if visible at all. So, the designers may need to not only make the word change color, but also make them bigger, add a sound, and even send a vibration to the controller.
This type of accessibility translates to the web design field in a similar way. Although things like sound and size in a menu would only be found in some sort of interactive (usually Flash) display, web designers need to keep in mind similar things, like adding alternative text to pictures for those who cannot see them, and generally making a site that conveys all necessary information no matter who is using it.
Accessibility is all about making sure anyone can use your product or service. In an office building, this means having a ramps and elevators. In a video game, it could mean having subtitles. In web design, it might require alternative text in image elements. No matter what the situation, accessibility means keeping everyone in mind.