It's easy to remember the difference between "dioecious" and "monoecious" plants if you study the prefixes of the respective terms. Let me explain:
Let's say the male reproductive organs of a plant species appear on certain plants of that species, but not others. Instead, those others (and only they) bear the corresponding female reproductive parts. The plants in that species are said to be "dioecious." The di- prefix indicates "two" in Greek (as in two separate plants are needed, in this case) -- that's how you can remember the meaning.
What does that mean in practical terms? It means that you must have at least one male plant growing in or around your landscaping for the fruit-bearing female plants to be pollinated. Holly shrubs are an example of such dioecious plants.
By contrast, you don't have to worry about providing a partner in the case of "monoecious" plants. They bear both male and female reproductive organs on the same plant. Most of our landscaping plants fall into this classification; we take it for granted as the "normal" state of affairs. The mono- prefix indicates "one" in Greek, which is a simple way to remember the difference between "dioecious" and "monoecious" plants.