In Sailor Moon, Monster of the week is a colloquialism used to refer to monster sent by a major villain's henchmen (such as Jedite or Emerald) to help them steal energy for their particular purposes.
The term "Monster of the Week" is said to have been coined in the 1960s by the writing staff of the 1969 television series The Outer Limits in attempt to differentiate themselves from The Twilight Zone, another genre television series. Monster of the week was a play on the term "Movie of the Week", during the time wherein movies were produced to be aired on television or in the theaters on a weekly basis.
Sailor Moon series never explicitly refers to the monsters in any of the four seasons as "Monsters of the Week". Instead the term merely brings attention to frequency and number of monsters the protagonist, Sailor Moon has to fight.
"Monsters of the Week" usually only appear in one episode, and there is usually only one each per episode (although there are some exceptions). Most of them are destroyed by Sailor Moon using whatever her main attack is. Rarely, some monsters are destroyed by a Sailor Scout or someone else.
It is interesting to note that each season has one monster of the week that plays a major role. In Sailor Moon, Zoycite's monster Housenka kills Neflite, one of the more major characters. In Sailor Moon R, the Cardian Racy destroys Sailor Moon's locket, only for Queen Serenity to restore it and make it more powerful.
In Sailor Moon S, Kaorinite's monster Senishenta appears in two episodes before she is destroyed. In Sailor Moon Super S, ParaPara's monster Mr. Magic Pierrot directly kills Hawk's Eye, and indirectly kills Tiger's Eye and Fish Eye by destroying Serena's dream mirror, forcing them to give up their power to rebuild it (though all three are revived, and Mr. Magic Pierrot destroyed).
Most monsters of the week are female, though there are some male monsters, such as five out of the Seven Shadows, a few Cardians, the droids Doom and Gloom, and any Remless working for Fish Eye or JunJun, plus Mr. Magic Pierrot.
Sailor Moon (season)
In Sailor Moon, the monsters are Negamonsters, sent by the Negaverse to drain energy. Zoycite and Malachite transfomr people into Negamonsters, where they must be healed by Sailor Moon. Negamonsters summoned by Jedite and Neflite are usually destroyed by Sailor Moon.
Sailor Moon R
In Sailor Moon R, there are two types of monsters. The first is Cardians, sent by Alan and Ann to gather energy for the Doom Tree. The second is Droids, sent by the Negamoon Sisters and Emerald to help them take over Crystal Tokyo. Most Cardians and droids are destroyed by Sailor Moon's Moon Scepter Elimination.
Sailor Moon S
In Sailor Moon S, the monsters are Daimons, or Daimon Heart Snatchers. They are sent by the Bureau of Bad Behavior to extract Pure Hearts. Most of them are destroyed by Sailor Moon's Moon Spiral Heart Attack or Rainbow Moon Heart Ache.
Sailor Moon SuperS
In Sailor Moon Super S, the monsters are Remless sent by the Dark Moon Circus to defeat the Sailor Scouts whenever they try to stop them. All of them are destroyed by Sailor Moon's Moon Gorgeous Meditation.