It means "like a monster," but it also means "abnormally huge," perhaps because we do not typically designate small things as monsters unless they are behaving very badly.  A long time ago it was used to describe  strange or unnatural events or people.

Today, we use this word to describe having an extraordinary often overwhelming size (gigantic) and in some cultures is even used to describe something very great  or awesome!!!!

The pattern of monstrous (where "monsterous" might be expected) is a regular transformation in many words, including disastrous and lustrous.