When you want, you want 'something'. And that something may be stated simply as a noun: "I want a book", which in Swedish is quite easy because you can't have a noun after "vill", you always have to state that you "want to have". So:
"I want a sandwich" = "Jag vill ha en smörgås".
But that 'something' that you want, may be an action (a verb), and in this case, you have two options.
If the Subject of the second clause is the same as the first one's, that is, I want that I die or HE wants that HE goes to Stockholm, you use the infinitive form as in English.
"Jag vill dö" = "I want to die"
"Han vill åka till Stockholm" = "He wants to go to Stockholm".
However, if the Second Subject is different from the First one, then you have to use the relative clause structure, that is:
"Jag vill inte att du dör" = "I don't want you to die" (lit. I don't want that you die).
"Jag vill att du läser min bok" = "I want you to read my book" (lit. I want that you read my book)
Hope that helps!
I think “att” is here because, unlike English, I think Swedish has to have a conjunction to fill in the empty spot. We never use a conjunction when we say “I don’t want you to die” or something; it just seems weird that we put an infinitive verb at the end instead of just having a conjunction.
But you can say "I don´t want THAT you die", which, in this case, would follow the same extructure as in the Swedish sentence. Thing is "I don´t want you to die" has a subordinate final sentence, which is seen by "to". Note the "difference" here: "I don´t want you to do those things" and "I don´t want you do those things"- Almost same meaning, unless by the fact that in the first, having a subordinate final sentence, there´s the detail of future, potential, etc. and in the second one there actual action happerning "right now", so to say.