Vipassana is a meditation technique originally taught by the Buddha. It is meant to promote peace and harmony in ones life and eliminate the agitation, irritation, and disharmony one often experiences. The link above provides a summary of the principles underlying the technique. These principles are discussed at greater length in the book The Art of Living (note: this is unrelated to the Art of Living courses one hears about). The technique itself is taught in a completely free 10 day course held at various locations around the world (see the Vipassana site for details of a course near you).
I was introduced to Vipassana by my father. He has been practicing Vipassana for over 15 years now. My father is the most spiritual person I know---not religious in a traditional sense, but rather someone who was always searching for the higher truth. He says that of all the things he's learnt, Vipassana has been by far the most beneficial. This is high praise indeed.
I've read The Art of Living and have heard a series of lectures by S. N. Goenka, the person who has been instrumental in spreading Vipassana in India and around the world. From everything I've read and heard, the technique sounds very compelling. There's no hocus-pocus. It's a very concrete technique, with very concrete reasons for why it works. I'm not going to try to distill the essence of the technique here; for that I refer you to the above sources for an authoritative and comprehensive treatment (but I'm happy to talk to you about my understanding if you're interested).
An important point, emphasized by Goenka, is that reading books or listening to lectures is no substitute for actually practicing Vipassana. A good friend of mine, Raj, recently had the good fortune of actually attending a Vipassana course. Here's what he writes about his experience:
Just got back from Vipassana. 11 days of living like a monk in silent meditation. It is wilderness survival training for your mind. Training your mind to survive on its own and manage your anxieties, fears and other strong emotions without the support of conversation, reading, television or any contact with the outside world. You learn how to control your subconscious mind to recognize and control your cravings, desires and attachments. It is frightening to realize the depth and strength of the roots of your cravings. As you try to teach your subconscious mind to be equanimous to cravings, these deep rooted desires literally surface in waves that get amplified as they bounce around in your head without any of the usual distractions to dampen their intensity. Your mind feels like it is going to snap, much like the suspension bridge bearing the army garrison that did not break file. The first few nights I literally woke up sweating in my eight by eight cell surrounded by the ghosts of physical manifestations of my cravings swimming around me in the darkness. It starts getting better after about the fourth day.
That sounds like a pretty intense experience! (And, yes, he's a rather good writer!) I've been wanting to do the course for some time now. I almost attended a course back in 2004, but a minor emergency at the last minute intervened and I chose not to attend. Now, almost 4 years later, I'm finally getting around to fixing this omission : I'll be attending a course starting next week (assuming, of course, there are no emergencies this time!).