Zazen is seated Zen meditation.
The idea is that you sit on a cushion, legs crossed in the lotus (or half lotus) position, hands together and thumbs touching in a mudra, and you let go of your thoughts. When thoughts arise, you don’t fight them, but you observe them and let them pass.
Sometimes there’s a specific thing to focus on, like your breath, or a koan. Other times, as in shikantaza zazen (which I practice), there is no focus – or rather, you focus without fixing on anything in particular. You generally do this for 20-30 minutes.
The idea is that if you do enough zazen, gradually you get to know yourself – which is another way of saying that you see the capital-T Truth, aka realization, awakening, or enlightenment.
I’ve been doing a lot of zazen lately.
I have a list of daily activities: chores around the house, Rosetta Stone, reading, writing, doing this blog, etc. But pretty much anytime I’m not doing one of those, I’m either sitting zazen or listening to a talk about Zen.
You might say I’m getting obsessed. Which is kind of funny, since Zen is partly about doing away with obsession. But part of the Eightfold Path is Right Effort, so I think it’s allowed.
Tomorrow I may head up to the Buddhist Temple of Toledo for their Wednesday service. If I do, I’ll let you know how it goes!
Anybody have any questions about meditation, zazen, or Buddhism generally? I’m far from being a teacher, but I’d be happy to answer the best I can.
Brian D. Buckley 
“When thoughts arise, you don’t fight them, but you observe them and let them pass.”
That’s how I was taught about Quaker Meeting for Worship (which is silent, and somewhat like a group meditation). When people hear about silent meeting, they often think they’ll need to stop thinking, which is impossible, but I always explain it, in pretty much the same words you’ve used here.
Cool! Very interesting.