This will have to be the subject of a longer blog post at some point. For now, let me quote the definition I wrote for the Contact Improv LA Web site:
Contact improvisation (or CI, or “contact”) has always been difficult to define, in part because it’s intentionally undefined, in part because it continues to evolve and change.
However, one definition might be that contact improvisation is a social dance that arises out of modern dance traditions. One of its central principles is a rolling point of contact between two (sometimes less, sometimes more) people through which both dancers give and share weight. It’s somewhere between tango, modern dance, aikido, wrestling, gymnastics, and none of the above, and usually takes place without music. People dance contact in any combination of genders, there are no “steps,” and it’s entirely improvised.
You can find a few more definitions at contactimprov.net.
And here’s a few favorite video clips that may help give a basic idea:
Stefan Fabry & Shel Wagner Rasch in performance:
Steve Homsher & someone at a jam (CI36):