Assuming there's not a mechanical problem (debris in the way, damper partially or completely closed, chimney cap damaged/missing and allowing wind to blow down the chimney, etc) then the phenomenon is as follows:
At a given pressure, cold air is more dense than warm air, and tends to fall. Warm air is less dense than cold air and tends to rise. The same phenomenon on a much larger scale is the cause of wind. A chimney is too small for both to happen at once. Either your house will draw cold air down the chimney and vent the excess air through the slight drafts that all houses have, or it vent air out of the chimney and draw cold air through those drafts. The intended function is the latter, but it's hard to engineer a passive chimney that's open on both ends that only does one or the other.
You can feel this: with the stove safely off and cold, open the damper and put your hand or a piece of tissue paper near the flue. You will feel or see a breeze flowing either up or down the chimney.
If the hot air from the fire rises up the chimney, as intended, it will rapidly warm the whole air column in the chimney, which will then rise, carrying the smoke out of the house.
However, if the hot air from the fire escapes out into the room instead, the cold air outside will flow down to fill the low pressure region. Wind will blow following the pressure gradient, keeping the chimney cold and the hot air from the fire (plus smoke) blowing out into the room.
To prevent this from happening (again assuming there's not a mechanical problem), you can use a hand-held electric heater or use tongs to hold a bit of burning kindling inside the flue opening after opening the damper to pre-warm the air column in the chimney and start the airflow moving in the desired direction before lighting the fire.