The Malefic monsters were introduced in the Yugioh 10th Anniversary film, Bonds Beyond Time, as a series of cards used by the villainous Paradox. They are essentially corrupted versions of iconic Yugioh monsters, mainly dragons such as Blue-eyes and Red-eyes. In the original Japanese, they were known as the 'Sin' monsters (a pun on the Japanese word for 'truth', pronounced Shin, a play on words which represented Paradox's twisted worldview that these corrupted monstrosities were the true Duel Monsters), but was changed to 'Malefic' by the censors at 4kids in their tireless effort to make everything boring. The Malefic monsters all share some things in common- they require a Field Spell to be active, there can only be one Malefic monster on the field at a time, and are summoned by banishing the original 'good' version of the monster.
They also, basically, suck. At least, a lot of the Malefic monsters do, since their trading card game incarnations come with a whole host of drawbacks. Cards like Malefic Blue-eyes White Dragon and Malefic Rainbow Dragon need you to banish the original monster from your Main Deck, which can result in a ton of dead draws and make for a very inconsistent deck (don't even get me started on Malefic Red-eyes Black Dragon, which is just a terrible card). Not to mention, Malefic monsters stop your other monsters from declaring attacks. That's not to say that the Malefic archetype as a whole is worthless- on the contrary, a skillfully built deck can utilize the best aspect of the Malefic monsters (the ability to effortlessly summon high level monsters), while simultaneously working around their negative effects and limiting the opponent's ability to respond.