The Firecracker is a thrown Mongol noisemaker that pulls several enemies toward the bang. It is the group version of the Wind Chime, good for clearing a path or bunching guards up for an ambush.
Throw it in any direction away from your route. While the guards head for the noise, sneak past them or come up behind them.
Bunch enemies up with a Firecracker, then follow with a Black Powder Bomb or Sticky Bomb while they stand together. It doesn't hurt anyone, so its value is all in where you send the guards.