Donatello's Laser-Guided Missile Launching Staff is a weapon that Donnie designed to, once again, attempt to update his bo staff. However, he accidentally set it off prematurely and, we are led to believe, it exploded. (We can't be completely sure as the episode ended with the turtles running for their lives.)
As the name implies, it is a staff fitted with a laser guided missile system. It also seems to be somewhat unstable.