The 2 pictures above show different stages of deterioration of a masonry chimney that is oversized for the heating appliances that it is venting. When you have your furnace or boiler upgraded to a more efficient model, you get more usable heat and waste less heat up the chimney. If the chimney is not the proper size for the new heating appliance, the gasses will condense inside the lining (as in the picture on the left). The acids in the condensation combined with the freeze/thaw effects of winter will deteriorate the masonry lining (pictured on the right). As a masonry flue deteriorates like this, pieces of the lining fall and block the base of the chimney which blocks the flue and does not allow the gasses to vent. This can cause carbon monoxide to spill into the house or a loss of heat.
If you have upgraded your furnace without having your chimney relined, this process is likely happening in your chimney. Schedule an inspection of your furnace chimney to determine if a relining is necessary.