Below are definitions that I've seen; there may be less strict definitions under which monoecy (the noun form of 'monoecious'). and hermaphroditism would be the same thing.
Dioecious: Although rarely used for animals, one could say that human are dioecious because each individual produces only one type of gamete. In a dioecious species, some individuals are males and others are females.
Monoecious: In monoecious plants, individuals carry both males and female flowers but not flowers that can produce both female and male gametes.
Hermaphrodite: Hermaphroditic plants have flowers that can produce both male and female gametes.
Then, there are many other fancy terms such as dichogamous, gynomonoecious, subandroecious, heterostyly or androgynomonoecious! Plant mating systems are fantastically diverse and complex!
Some of these terms are defined in The Evolution of Sex Determination, which is very pleasant to read. For shorter articles, consider Barrett 2002 or just Wikipedia > plant reproductive morphology or Wikipedia > dioecy (the noun form of 'dioecious').