A monster, as defined by Merriam-Webster, is as follows:
1 a : an animal or plant of abnormal form or structure b : one who deviates from normal or acceptable behavior or character
2: a threatening force
3 a : an animal of strange or terrifying shape b : one unusually large for its kind
4: something monstrous especially : a person of unnatural or extreme ugliness, deformity, wickedness, or cruelty.Based upon these four definitions, one can define what makes a monster in many different ways. Since your question is posed under Frankenstein, it would be pertinent to address the monster depicted in the novel first. Victor's monster can be justified as a monster based upon all four of the definitions given. The monster deviates from the acceptable form of what one considers human. Throughout the story, the monster becomes a threatening force. Lastly, the monster is also seen as possessing a terrifying shape and extreme ugliness. That being said, there are also other ways society defines a monster when adhering to the definitions provided. People who commit crimes so hideous against society are, many times, deemed monstrous. For example, in Walter Dean Myers' novel Monster, Steve Harmon is considered a monster simply based upon the fact he is being tried for murder. Lastly, is the supernatural monster. The monsters depicted in epics like Beowulf (Grendel), current nonfiction texts like Twilight (Edward and Jacob), and the mythological texts like The Labors of Hercules (Medusa) all are defined by the characteristics above.
Therefore, a monster comes in many different packages. The defining of a monster is simply based upon a personal interpretation of what they deem monstrous.