Pigeon drop is a confidence trick in which a mark or "pigeon" is persuaded to give up a sum of money in order to secure the rights to a larger sum of money, or more valuable object.
In the process, a "stranger" (who is part of the scam as a confidence trickster, a confederate) puts his money with the mark's money (in an envelope, briefcase, or sack) which the mark is then entrusted with. The money is not put into the sack or envelope, but is switched for a bag full of newspaper or other worthless material. Through various theatrics, the mark is given the opportunity to make off with money without the stranger realizing. In actuality, the mark would be fleeing from his own money, which the con man still has (or has handed off to an accomplice).
In the opening scene of the 1973 film The Sting, Johnny Hooker (Robert Redford) and Luther Coleman (Robert Earl Jones) pull a pigeon drop on a numbers runner for Doyle Lonnegan (Robert Shaw), resulting in the murder of Coleman. This provides the motive for Hooker to seek out Henry Gondorff (Paul Newman) to run the titular sting on Lonnegan.