A monster is most often a villain, right? Now the best villains have well-thought-out backstories that explain their villainy. For Magneto, it's the way he and his parents were treated by the Nazis. For Dr Doom, it's his philosophy, his need to place the same order and peace on the whole world that he enforces in Latveria. The Joker is simply insane. Hannibal Lecter kills because he can and because his victims mostly deserve what he does to them. So you should create the same kind of backstory and motivation for your monster.

Of course, your monster needn't be a villain. He can be a victim, like King Kong, or a 'hero' like Godzilla.

Care and attention is why Mary Shelleys' 'Creature' (something that was created, in the old meaning) is so much more compelling than the flat-skulled, bolts-in-the-neck 'Monsters' presented by so many film-makers.