WHAT IT IS
It's called Marbling because the results look like the swirls of color in marble stone. It's been around as an art form for a long time - old books sometimes have marbled end-papers. The idea is that you float fabric paints on the surface of a thick liquid that you prepare (called "Size"), kind of like oil on water. The floating paints can be swirled and mixed into patterns. When you lay a treated shirt, piece of fabric or paper down on top of the paint, the paint adheres to the fabric exactly where it touches. The swirly patterns of colored paint are tranfered to the shirt or fabric.
Each design is unique and can never be repeated. As a technique, it's both easy and hard. It's easy to do, great fun for kids and safe. It's hard in that the more you do, the better results you will get and the difference between your early designs and your later designs will be very noticeable.