It means you haven't got the fonts installed on your home computer that you used on your document in your class computer. You need to either install your class fonts onto your home computer or select new fonts on your class computer that are the same as your home one (or reverse!).
Actually, that may not be necessary.
Instead of just copying your document, use the Package command from the File menu to create a package folder and check the box to include fonts (and the IDML file in CC versions). This will create a Document Fonts folder alongside the file and when the file is opened it will use the fonts in that folder for editing and printing.
Though you will need a license for the fonts to do that, right?
Not everyone starting out realise just how many fonts there are. It isn't that all computers have the same fonts. There are hundreds of thousands of fonts, perhaps millions. It's like trying to find a book that is both in the school library and at home. But then, fonts are sold and licensed - you can't just copy them between computers.
You need to choose carefully. This is a crucial part of your DTP education, as important as what to click in InDesign...!
Apparently Adobe doesn't view document installed fonts as a licensing issue (or if they do, the legal team has said the liability ends with a warning message). If the fonts are compatible, ID will use them, licensed or not, if they're in the Document fonts folder.