What is the meaning : if we pack a Proton and an electron together in a small volume the combination does not attract or repel another electron or Proton placed at a distance .

It does, if the test charge is located anywhere but in the plane perpendicular to the axis joining the electron and proton (which I presume you are holding fixed to form an electric dipole). The electric field of an electric dipole has the same shape as a magnetic dipole’s magnetic field, which you’ve probably seen. (If not, put a piece of paper over a bar magnet and sprinkle iron filings on it.)

But the dipole field is much weaker (at a distance) than the monopole fields of either charge, because it falls off as the inverse cube of distance.

Source- Jess H. Brewer(Quora).