I should point out that there's no indication The Witness will come to the PC. It has been seen working on the Xbox 360 but it has been said that it will be released on multiple platforms.
So what is it? As far as has been seen, the player wanders an island from a first-person perspective. The island is littered with points of interest - a bungalow, a lighthouse, a gazebo, a raised platform etc - with puzzles scattered around. The puzzles seen so far as kind of connect-the-dots logic puzzles but I think we can expect more than that. A lot of time and effort has been poured into the graphics engine, making the world beautiful and shadows pass realistically across the ground and walls as the sun crosses the sky. The graphics themselves are apparently, as of late August, placeholder but they give a good sense of the atmosphere the team are working towards.
The immediate point of reference is Myst, or more recently Dear Esther which of course lacked the puzzles and added the voice-over narrative. If anything it looks like a room-escape puzzle that forgot to be bound to a single room.
The Witness was showing at PAX this weekend, alongside my favourite in-development indie game SpyParty and Monaco. According to the games' development blog, the idea was to keep it pleasantly low key and actually reduce the attention it got so players could take as long as the required and/or desired. I wonder if they also didn't want to include anything that could influence the players and spoil any feedback they might get.
All that was known of The Witness last time it passed through my awareness was the at the top of this post. A door with a blue square on it at the end of a dark corridor is very little to go on but already excitement was growing. Until the game is released sometime late in 2011, I predict that excitement is going to blossom and boom to ridiculous (though not necessarily undeserved) levels. This is definitely one to watch!