Book of Vile Darkness
The Book of Vile Darkness is a term from Dungeons & Dragons that can refer to either of two things; an in-game magical item, or a pair of splatbooks that exist for Dungeons & Dragons 3rd Edition and Dungeons & Dragons 4th Edition. In case its edgy name didn't give it away, it's all about the EVIL side of things, with a goodly counterpart in the Book of Exalted Deeds.
The Magical Item
The Book of Vile Darkness has shown up in multiple editions of D&D, and is essentially a compilation of notes and musings on the nature of evil by some of the most wicked and profane beings in the Multiverse; Vecna is usually described as one of the first editors to craft the Book of Vile Darkness. In general, it's of great use to an evil spellcaster (or at least a cleric), but is hazardous to the body, mind and soul of anyone who isn't evil.
3e Splatbook
Released for 3.0, the Book of Vile Darkness was a sourcebook on evil, containing a mixture of the authors' personal musings on the nature of evil and how to use it in your games of Dungeons & Dragons, either as adversaries for your party or by running an evil PC campaign yourself, and mechanical support for that goal in the form of new rules, equipment, systems, monsters, gods, etc.
The book is widely regarded as something of an eye-roller, as it handles its themes clumsily at best. It was, however, the original splatbook for 3e to feature many classic "villainous" monsters, such as Demon Princes and Archdevils.
Also has some serious balance issues. Some alternate options for bestow curse. While most are pretty nasty social penalties and not really of note since the default options include "do nothing half the time", but also "Target is rendered sterile." Since curses are relatively easy to remove (just cast the opposite spell), this tends to be an advantage to most Adventurers. The disease Festering Anger is also introduced which damages Constitution in exchange for an increase in Strength with no ceiling. It's as easy to break as healing the constitution damage (a mere second level spell, or first if you know what you're doing).
4e Splatbook
Much like its 3e counterpart, 4e's Book of Vile Darkness was a sourcebook on evil in Dungeons & Dragons, divided into two physical splatbooks. The DM's book is full of advice for DMs on how to use evil or to run evil campaigns, complete with monsters, cursed items and other foulness to use against players. The Player's book, in comparison, is all about new PC goodies for malevolent (or at least seriously antiheroic) PCs, including character themes and Paragon Paths.