Flagging (sometimes called fan dancing) is when you take a piece of cloth and spin it about in the air in time to music. Usually you use a pair of them, hemmed with drapery chain on the edges near the leading corner to give it some weight so it can cut through the air. Typical flags are a few feet on an edge, up to really big ones that can be 5 feet or so. You have day flags that are reflective and look good in the sunlight outdoors, and club flags that are often fluorescent to use in a dark dance club. All tend toward vibrant colors, tie-dye patterns, etc. Lightweight, sheer fabrics are a must.
There are many techniques, some of them very difficult. The basic one is making a figure-8 with your hands so the flags spin constantly in front of you, always chasing each other in an infinite game of cat and mouse.http://www.seattleflaggingboys.com/
has a few pictures, but it's a pretty out-of-date site. Still pictures never look good - you have to see the flags spin to understand the appeal. This is the best pic I could find on that site: