I think "accessibility" makes sense when you're talking about the basics. If you have to read through a manual and have a degree in space rocket science in order to figure out how to move your dude, then the game is a little inaccessible. (Not that I have a problem with games being inaccessible. Easy to learn and hard to master, or hard to learn and hard to master -- it's really the hard to master part that is most important.) But these days when people talk about accessibility it's as if every part of the game must be immediately accessible. Mastery of the game must be accessible (i.e. it must be a shallow game), or at the very least all those things you get from mastering the game should just be given to you at the start.
I think there are two uses of the word accessible here. On the one hand, there can be a sense of "dumbing down" or making a game too easy in order to appeal to a wider audience. That might mean a real sacrifice to your vision or the quality of the game, and/or might even be seen as a bit insulting. But there's another sense, which I think is what Terry was meaning:
Many people have disabilities or conditions that make it difficult or impossible for them to play many games. One easy example is color blindness; there was a writeup recently I think on gamasutra talking about how certain puzzles in BioShock 2 are impossible or near-impossible for a color blind person to defeat. Not nice if you're color blind!
Other people may not have the motor control required to beat certain parts of an action game. So a slow-motion mode or an invincibility mode can be really helpful for them and allow them to enjoy a game they might not otherwise be able to.
Anyhow, here is the article that I think states things more clearly than I am doing here:
http://www.retroremakes.com/access/If you think of it, it's especially cool that a super reflex-challenging game like VVVVVV contains accessibility options for people who might already have challenges with their reflexes in day-to-day situations. This is exactly the type of game that such a person would be normally written completely out of, so it's nice to think of it opening up to a new audience.
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