Phase margin and stability
"In Control Systems, an open loop Transfer Function having poles in
  Left half plane, should have positive phase margin and positive gain
  margin to ensure closed loop stability."


I would point you to this site where I took the picture below: -




A positive gain margin means that the gain magnitude has dropped below unity as the phase angle of the output reaches the point where it is fully inverted (the oscillatory point). This means it is stable because there cannot be enough gain to produce oscillation when used in a negative feedback control system.
A positive phase margin means the the phase angle of the output has not yet reached full inversion (the oscillatory point) as the gain magnitude drops to unity. This also means it is stable when applied within a negative feedback control system.