The Meat Puppet program is a program that brainwashes people and turns them into Meat Puppets. Then they work in The Movement. Jov Leonov, master of the Psi power of Mind Control, is the creator and director of the MP program.
The process of creating Meat Puppets varies based off of which meat puppet is being created. It seems that some of the processing is performed by robots as one of Nick's squad, Sanders, was shown having their control collar fitted by an automated process. Labcoats have been seen working on meat puppet corpses as well.
Once a Meat Puppet of any type is created, the individual has effectively had their mind wiped and their previous loyalties no longer exist. Dedicated UN soldiers, such as the men in Nick Scryer's unit at the refinery, are observed in the game to have been turned into blindly loyal soldiers of the Movement, willingly doing anything they are ordered to.
The reprogramming process had "taken some time to perfect" according to Leonov, but once it is finished, it is irreversible. The Meat Puppet program's methodical process of reprogramming captured individuals, notably soldiers, was ended after the abandoned nuclear missile silo occupied by the Movement was destroyed by a number of bombs set by Nick Scryer.