Here's the definition from the official Zentangle site:
Zentangle is an easy to learn method of creating beautiful images from repetitive patterns. It is a fascinating new art form that is fun and relaxing. It increases focus and creativity. Zentangle provides artistic satisfaction and an increased sense of personal well being. Zentangle is enjoyed by a wide range of skills and ages and is used in many fields of interest. It was created by Rick Roberts and Maria Thomas.
I know this doesn't quite explain it but it is something you have to experience to really know what it is.
I was skeptical when my friend, Suzanne McNeil, first told me about it. After taking a class with her, I was hooked and now I'm completely addicted. It's a wonderful addiction, though. It is so relaxing after a stressful day. If you're interested and want to know more about it go to http://zentangle.blogspot.co