Zentangle is the term now being applied to an art form created by the folks who run the web site http://www.zentangle.com/. No one would ever claim that this stuff is great art or particularly profound, but it could be fun for people with time on their hands. And it might be useful as a means of generating patterns and textures for use in other art projects.
If you want to create Zentangle, I would suggest the use of a Wacom Inkling; that way, you can more easily create digital art, and the images can even be output as scalable vector art.
To get an idea of what is involved in making Zentangle art, watch this video. As you can see, it's basically doodling, but with particular aspects which lend it to the creation of line art patterns.
I think that the term Zen is used by the inventors of this form of art because they wanted to emphasis the meditative aspects. It's possible that doing this might have some serious art applications, in the sense that it would enable practitioners to get into the "right brain" thinking mode so crucial to the teaching methods of Betty Edwards, author of Drawing On The Right Side Of The Brain. For those who want to learn to draw more realistically, I highly recommend that book, which is very helpful to those willing to wade through a bit of text which explains the scientific basis for Edwards' teaching method. The text itself might be a bit of a turnoff for people who eschew theoretical knowledge in favor of hands-on knowledge, except that it is accompanied with before and after drawings which show that her teaching method works.
If you have ever fallen prey to the false idea that artistic talent is something you either have or don't have, and if you've ever felt frustrated by you inability to draw things realistically, you should pick up a copy of that book. Even better, if you have a chance to take a drawing class based on the theories and exercises in the book, you should do so, just as I did in the 80s at the Boston Center for Adult Education when I still lived in Boston. If you cannot take such a class, then at least get the related workbook. Or watch Betty in the video at http://youtu.be/U5xG2ieSe_w.