The Feynman propagator is a vacuum time-ordered two-point function, with the conventional overall factors stated. For a free real scalar field, has momentum-space form in the usual Minkowski convention.
Time ordering places the later field to the left, and the pole prescription selects the vacuum boundary condition. The propagator is the Green function used for internal lines in perturbative amplitudes; it is not a directly measured probability for a particle to follow a particular path. It can be nonzero at spacelike separation without enabling superluminal signalling. Causal response is instead organized by the retarded Green function and local commutators, so these different two-point functions must not be interchanged.
New to topics? Read the docs here!