The jar of souls is a rare drop from Cerberus. Using one on Adam will initiate a dialogue in which he will claim that he's been looking for souls, and reaches in the jar to take one.
In addition, using one on the soul altar in Arceuus will cause Sister Soul Jar to appear, performing the Dance emote.
The jar can be used on a boss lair display in a player's Achievement Gallery to have a display of Cerberus. Doing so requires killing her at least once.
For an exhaustive list of all known sources for this item, see here