I searched on Google and I found this picture. My question is, could you explain to me exactly who is Soulfire Darkseid? What is the Soulfire, how does Darkseid acquire it, and what does it grant Darkseid? I heard it is power, but is it power like the Anti-Life Equation to Darkseid? I'd like to know. Also, what issues is Darkseid Soulfire? Thanks if you can tell me.

Its from the "Death of the New Gods" story by Jim Starlin in the last one or two issues.  A tale many (if not all) fans of the New gods I know of would prefer had never happened and a story that for the most part was generally ignored by other writers.  The main reasons being for the plot holes and Starlin disregarding many long-established facts about the New gods and twisting their personalities into a story he could write among other reasons.
 
In the story Darkseid stated it has been an experiment Desaad had been working on one time that failed to produce the desired results so it was abandoned.  Darkseid later used it against the Source.  The Source had been killing New gods and capturing their souls because as a power source the souls of New gods were unique and unrivaled.  This power greatly multiples with each soul.  Two souls would not be 2x as powerful.  It would be more like four or five times as powerful.   Darkseid discovered the Source's stash and stole the souls .  The soulfire formula granted him access to the power of those souls making him even if not superior to the Source, the creator of the New gods and a supposedly omnipotent being. The battle with the Source was underwhelming as far as these powers go, but it was enough to tear a hole in reality and Superman admitted Darkseid was beyond him at the moment.  Darkseid even defeated the Source and stated he was not supreme.  Darkseid only lost because of the necessary story reason Orion’s soul was able to tap into the same power forcing Darkseid to flee.

So, it was supposed to make Darkeid omnipotent by tapping into the power of all of the souls of the New gods.   It did not come across nearly that impressive to me, but it might have just been the story.   “Death of the New Gods” was al in all considered a letdown that has been ignored and forgotten.

The following link includes a few scans of Darkseid discussing it himself:

http://image.politicalbase.com:8000/forums/battles/33/dark-schneider-vs-darkseid-sff/313983/?page=1