Ah, the million-dollar question...

Here is my current working definition, honed by countless practitioners:

SHORT: Where Aikido meets Yoga meets Tango with a dash of Zen meditation, you'll find this post-modern social and performance dance technique and practice, commonly called Contact, CI, or Contact Improv.

LONG: Contact Improvisation (CI) is a 40-year-old dance form which incorporates a fluidly moving body, awareness of breath, and trust in shared weight and momentum which can propel seemingly impossible moments of defying gravity. It is practiced as a source of performance partnering and as a holistically enlivening recreational activity. It is the only dance form, classic or contemporary, which has no pre-defined gender roles for action, and as such it continues to be both liberating and radical for all who practice it.

"CI fundamentals" (ie, its founding basic movement pathways) are not a set of static positions, but a series of embodied concepts about the utility and physics of the moving human body (Eg, falling, weight-bearing, levels of effort and pressure, disorientation, and levels of spatial/energetic/touch/choice awarenesses). If you have a body, you can do CI. Therefore, CI is less intimidating for those with no prior dance background. Fundamentals take about a month's worth of classes to learn, give-or-take one's own learning process (and eagerness!). And then, the subtleties and exultations of CI will keep surprising you with new lessons for a lifetime.

--Ali Woolwich, 2003 (revised in 2011).

And, from the originators of the form:
"Contact Improvisation is a dance form, originated by American choreographer Steve Paxton and Nancy Stark Smith in 1972, based on the communication between two or more moving bodies that are in physical contact and their combined relationship to the physical laws that govern their motion, gravity, momentum, inertia.
The body, in order to open to these sensations, must learn to release excess muscular tension and abandon a certain quality of willfulness to experience the natural flow of movement.
Contact improvisations are spontaneous physical dialogues that range from stillness to highly energetic exchanges, and leaves the participants informed, centered, and enlivened."

--From Caught Falling: The Confluence of CI, Nancy Stark Smith, and other Moving Ideas, by Nancy Stark Smith & David Koteen.

For more about Nancy Stark Smith and the world-wide CI network,
see the journal Contact Quarterly and associated books at:
contactquarterly.com