This product goes by many names: Soldering Wick, Desoldering Braid and Desoldering wick to name a few. If you've never used it before, prepare to meet your new best friend.
The product was developed after the World War 2 by Army Air Corps technicians who would strip the copper braid from coaxial cables, dip it in solder flux and then use it for desoldering. The wick is made of fine braided copper which soaks up solder using capillary action. It is primarily used for desoldering but also comes in handy for soldering surface mounted components by hand.
This wick has a width of 2mm and comes in a handy 1.5m (5 ft) spool.