The jar of miasma is an item that can be obtained from using the unsired, dropped by the Abyssal Sire, on the Font of Consumption. Players have a 13/128 chance of receiving one when doing so. As an unsired is a 1/100 drop, this effectively makes the chances of obtaining a jar 1/984.
The jar can be used on a boss lair display in a player's Achievement Gallery to have a display of the Abyssal Sire. Doing so requires killing him at least once.
For an exhaustive list of all known sources for this item, see here