Dark Essence is an etheral substance that clings to people and objects that have come into contact with The Darkness.
Every time a horrific event occurs—whether it's caused by evil actions or just a tragic accident—there's a trace amount, an echo, of the pain and grief caused by the occurrence that manifests and clings to the objects surrounding it. Those aware of this lingering substance call it Dark Essence, and it can be found to this day in the prized possessions of infamous murderers and tyrants, the remnants of disasters, and within the very hearts of malevolent individuals. What's more, it can be utilized to great effect if one knows where to start digging.
In The Darkness II, Dark Essence acts as a kind of currency that Jackie can spend to augment his already-impressive array of dark and gruesome powers. One important way that he can obtain more Dark Essence is by finding the relics tied to both bad people and famous tragedies of the past.
Throughout his campaign against The Brotherhood, Jackie can also obtain more Dark Essence by slaying his enemies. When he executes foes with his Demon Arms or finishes them off skillfully using more conventional weaponry, he'll collect some of the essence that they leave behind; if he consumes their hearts, he'll get even more.
Once he's obtained a sufficient quantity of Dark Essence, Jackie needs to find a special shrine in order exchange this essence for new or improved Darkness powers. From his time trying to regain some control over his internal demons, Jackie learned from Johnny Powell how to become attuned to and make use of these talent shrines, and he even has one set up in his place of residence.