basically, in a nutshell, a quick answer is "Jedi Mind Trick" is mind control. In the Starwars films the jedi were sort of warrior monk types (very roughly without long overcomplex explanations!). One of their abilities was they were able to "implant ideas" and use mind control on people with weak minds / low willpower.
In the film some stormtroopers (military police types) stop a jedi, a young farmer and two (renegade) robots. When the stormtroopers ask for ID papers the jedi starts this whole "you dont need to see his ID papers" and "these aren't the droids you are looking for" stuff. The stormtroopers then repeat each sentence. Finally the jedi tells the stormtroppers to tell them to "move along".