It's actually a giant grass that propagates by rhizomes underground spreading out from the root mass. It's not much different than Hostas or Lilly of the Valley. It spreads outward and grows quickly so it works really well as a privacy screen. The trick is to keep it contained by constantly mowing down the new sprouts as they spread.
If you want to kill it, just mow it down and let the new sprouts emerge to about 6" tall and spray the hell out of it with Round Up. It might take a couple of cycles but you will eradicate it.