In English, desires, needs and preferences can be phrased in a variety of ways: I wish you would eat, I want you to go, I wish that you would move your car... but here is a structure you will often see in Italian:
Desire/need/preference/wish... + che + usually subjunctive
- Voglio che tu mi dica la verità/I want you to tell me the truth
- Spero che la volpe vada via/I hope the wolf goes away
- Pensiamo che non sia giusto/We think it isn't right
Think of che as a marker. That doesn't always show up in the English equivalents, but in Italian that is how you know something uncertain and most likely the subjunctive will follow.
This che business does change if the hopes and desires are for yourself...
- Lui vuole andarsene/He wants to go
- Io spero di vincere/I hope I win
- Noi pensiamo di essere i migliori/We think we are the best
- Mia madre preferisce bere caffè/My mother prefers drinking coffee
In my opinion DL has caused a great deal of confusion here by giving students a sentence that requires the subjunctive long before there is a clear explanation of this structure. They should change this sentence And while I'm at it,, they are also sowing confusion by mixing the use of e and ed with no explanation or rule to guide the students.. In both cases the discussions show considerable bewilderment..
The subjunctive is being used here! It is called Congiuntivo, and the conjugation is Mangi for TU, just the same as it would be in the present. http://www.italian-verbs.com/verbi-italiani/coniugazione.php?id=5931
others have pointed it out, but i thought i'd reply to you. romance languages do not use the same sentence structure as English in this case. what you'd say as "i want you to do something" (do being infinitive) in Romance would normally be "i want that you do something" (do being subjunctive). only in this case it happens the subjunctive is similar to simple present.
It's just a matter of what comes after it, really. This happens in all of French, Portuguese, Spanish, etc. In Italian, we can add a degree of separation to the expressions, however. If you wanted to say "I want what you want" you'd use "ciò che" or "quello che." Ask a native Italophone and they will often they you that you can use whichever sounds best for you or in the sentence, but that they mean the same and can thus be used interchangeably.
Heads up: mangi is a subjunctive form verb here, and its form happens to be the same as its indicative form.
People don't really need much grammar for their own language. If you grow up in a household that uses the standard dialect (whatever that may be) well, you know all the rules before your first grammar class, even if you couldn't verbalize them. But when you are studying another language you need at least the basic vocabulary to discuss the differences in the rules. In the scheme of the world's 1600+ languages, Italian and English are rather closely related as languages on close branches of the same tree, but there are striking differences. To the extent you can dissect and categorize the differences, you will find them easier to internalize. Of course nothing replaced lots of exposure in making what is right sound right.
If you make good use of Google or whatever search engine you like, it should help you. I am going to run down the basic definitions of the terms you identified, but googling simply "The Italian subjunctive" or "Italian imperative" most of the links would provide a simple definition of the term in general before looking at Italian examples. If you can phrase a query, you can gets lots of different approaches to the answer.
The subjunctive mood has only a small vestige in English, so your English grammar wouldn't have helped here much. The easiest place to see the subjunctive is with the verb wish. I wish there were more. The past subjunctive often talks about a contrary to fact situation. If I were rich... You know I am not from this. The present subjunctive just introduced doubt.
In Italian, the formal you uses capitalized versions of third person forms for the formal you. Third person pronouns are generally he/she/it (singular) and they (plural). So you can have essentially a third person imperative (command) for the formal you. But it is my impression that Modern Italian uses its formal address much less than other European languages, depending on where you are in Italy.
This is not a set expression. Whatever situation you might imagine for the English sentence, it would be the same. The scenario I just came up with
Tutti i miei dottori mi dicono che mangio troppa carne rossa. Ovviamente. (Loro) vogliono che tu mangi pesce. All my doctors tell me that I eat too much red meat. Of course. They want you to eat fish.
But as I said the point is not the actual "message" itself. It's how all the individual elements form together to carry that message that Duo is trying to teach. With this pattern you can construct many sentences. My husband wants me to get a job. His boss wants them to move.