If you're wondering what the term Black Mass means, it isn't actually explained in the film. It's taken from the book that the movie is based on, though the tag line does describe it as an 'unholy alliance' between the FBI and the Irish Mob, headed by the most notorious gangster there is.
Unholy is right. Jimmy 'Whitey' Bulger becomes an informant for the FBI which somehow lets him get away with the most heinous of crimes. Supposedly loyalty makes FBI handler John Connoly carry thru with the deception.
The audience will most take note of the transformation of Johnny Depp into an intimidating and frightening sociopath who somehow still goes to church and takes care of his family. His paranoia and cold demeanor makes for uncomfortable scenes when he carries out his murders and rackets. The film practically belongs to Joel Edgerton as well. His role as the FBI contact lets him display the most tense and even human of interactions in this movie that is almost without heroic protagonists. The other actors such as Benedict Cumberbatch, Rory Cochrane, Kevin Bacon, Corey Stoll and others play their parts well enough though not as scene stealingly good as the leads. Peter Sarsgaard almost does so by making the most of his short presence as an addict.
While the film has suspense enough in choice scenes, the progression almost becomes day by day, month by month and there isn't much to the rising action. There is no huge climax or spectacular showdown, if one is expecting such in a gangster flick. The story keeps a steady pace, with patches of excitement in between.
The film is based on historical events so who's to say what's altered for dramatic purposes. Black Mass could have had a more human angle but it would be difficult, coming from an inhuman monster like Jimmy Bulger.