Here are two example sentences in English: "I want you to paint the house" and "I wish that you would paint the house".
The che is "that". Expressing desires, wishes and necessities (actually, a lot of uncertain things) follows the same structure as "I wish that..." = spero che, voglio che, desidero che... Additionally, you'll often see it followed by the subjunctive.
I opened this page because I was pretty surprised to find the subjunctive so close to the top of the tree. In traditional courses they first teach most of the tenses in the indicative (present, at least the passato prossimo, conditional, future) before passing to the subjunctive. Of course this particular sentence doesn't really throw you into needing to know the new endings since in the "tu" form it's the same both in the indicative and the subjunctive. https://www.wordreference.com/conj/ItVerbs.aspx?v=mangiare
I take it you are suggesting, "Lui vuole tu mangiare una mela." This direct translation from English is disjointed and nonsensical in Italian. To say, in Italian, that one person wants someone else to do something, you have to use the subjunctive. However, if he wants to eat the apple himself, the infinitive is correct:
- "Lui vuole mangiare una mela." = "He wants to eat an apple."
This is because the English "He wants you to eat the apple" uses an infinitive construction, but Italian does not require it. That's the simplest explanation for now (and I realize it's not really much of an explanation).
Whenever you want to say, "Someone WANTS something to X" in Italian (or French for that matter), you must use the construction volere che + subjunctive.