Except in Italian you can say "Ho il burro" and it doesn't mean you have THE butter, just butter. That's what's confusing, it's not clear when they mean "I have/eat THE noun" and when they mean "I have/eat noun" because the article in Italian is almost always there, in these past lessons at least.
If you keep the mouse over "mangia", where duolingo corrects you, you are able to see a button with the text "conjugate". Pressing it will show you that in Italian verbs have a different form for each person and number, and also, which one you should use for the current case.
Io mangio = I eat
Lui mangia = He eats
Edit: As with the latest updates, the "conjugate" button doesn't seem to exist anymore.
I know the article inclusion happens more often in Italian than in English without affecting meaning. I have a question, though, about how to emphasize the article in Italian. For example we have this sentence which tells us of a boy who eats cheese. Fine and dandy. However, if i want to specify that the boy eats cheese to the exclusion of other foods, possibly fruit, that are on offer as opposed to general cases, in English i could say "the boy eats the cheese, the girl eats the fruit." How would this be expressed in Italian with the specifying articles?