Below are the definitions that I've seen but there may be less strict definitions under which monoecious and hermaphroditism would be the same thing.
Dioceous: Although it is rarely/never used for animals, one could say that human are dioceous. We are dioceous because each individual produce only one type of gametes. A dioceous plant species is a species where some individuals are males, others are females.
Monoecious: Monoecious plants are plants where each individual carry both males and females flowers but there are no flowers that can produce both female and male gametes.
Hermaphroditite: Hermaphroditite plants are plants where each flowers can produce both male and female gametes.
Then, there are many other fancy terms such as dichogamous, gynomonoecious, subandroecious, heterostyly or Androgynomonoecious! Plant mating system is fantastically diverse and complex!
In animals, we typically don't use the terms monoecious and dioecious, mainly because mating systems in animals are, despite already being quite complicated, so much easier than in plants!
Some of these terms are defined in The Evolution of Sex Determination and the book is very pleasant to read alltogether. Also, consider reading the short paper Barrett 2002 or just wikipedia > plant reproductive morphology.