Your front door likely has significant air gaps if you can hear every discussion taking place in the building hallway from the comfort of your sofa. Stopping the sound from entering by plugging these leaks will stop the chatter. In addition, since sound travels through the air, it will pass through any opening through which you can see the light.
Add a door sweep if your apartment door has a sizeable gap underneath it. Use a commercial-grade sweep sealed against the threshold by a thick rubber strip. Along with the noise, this will also aid in blocking out dust, insects, and draughts. Foam weatherstripping should be used to seal the sides and top of the door if the rest of it does not close snugly against the door jambs.