A drop gun is a spare weapon that you carry with you that can be "dropped" beside the body of the person you just shot. When the police come, it appears to have been a justifiable homocide (self defense).
Police officers have (fairly or unfairly, I don't know) been accused of using this tactic. Shoot a man who doesn't have a gun, and you can have disciplinary actions, civil lawsuits, criminal court proceedings, and even riots. Not fun. If an officer thinks someone has a gun, shoots him, and kills him but then finds no weapon, the incident investigation goes rather more smoothly if one merely "drops" a gun near the dead man's hand.