Whenever you see a sumo wrestler enter the arena before a bout, you will no doubt notice the stiffened strings hanging from the front of his mawashi (belt). Those are the sagari. There will always be an odd number of sagari, anything from 13 to 25 (depending on the girth of the sumotori).
When the sumotori gets ready to sit down, or step up on the dohyo - or, for that matter, when he crouches down before the bout starts (at tachiai) - he will carefully arrange the sagari to avoid dislodging or bending them. Once the bout is over he will most often remove the sagari if they haven't already been torn off during the fight. This happens quite frequently, and it's up to the gyoji (referee) to snatch the sagari from the ground and throw them aside.
The sagari are made of silk strings stiffened with a glue made from funori, a type of algae, and fastened to a length of fabric at one end. They are there to mark out the only part of the mawashi that it is illegal to grab on to: the vertical part covering the sumotori's privates.
My sources are, besides being glued to the TV whenever sumo is on, http://sumo.goo.ne.jp/eng and http://www.sumoforum.net/glossary.html.
That was the long explanation. The short, short explanation, courtesy of Pseudo_Intellectual, is:
"A string apron attached to a mawashi, hiding the naughty bits of a sumotori and preventing us from finding out after all this time do fat men get fat dicks?"