Think of the project file as a printed recipe. It might say, "take a stick of butter and mix it with a cup of flour and a cup of sugar, then add 2 eggs, etc." At the top of that recipe it *lists* the ingredients you need and how to mix them, but a recipe doesn't have any actual ingredients within it.
If you take your project file to another PC which doesn't have any of the media files (ingredients), there is no way to use that recipe. It would be like giving a recipe to someone that doesn't have any of the ingredients and also doesn't have a kitchen for following the recipe.
So whenever you want to share your creation and make sure they can enjoy it, you need to actually follow the recipe using your ingredients and bake them together into a final creation (a movie file). The movie file in .mp4 format is what you can share on another PC or with your instructor. They don't need any of your original source files and they don't need to have Movie Maker either.