“Qu’est-ce qui” does not translate to “what is it that”. It translates to “what”. “Est-ce que” is a fixed idiom, it’s one of the three ways of formulating a question:

• formal: verb-subject inversion, e.g. “Qu’as-tu fait ?”
• neutral: “est-ce que”, e.g. “Qu’est-ce que tu as fait ?”
• informal: same word order as a positive statement, e.g. “Tu as fait quoi ?” (for a yes/no question, the fact that the sentence is a question is only conveyed by intonation)

The word corresponding to what is either quoi or que. In simple cases, it’s que when the interrogative pronoun comes before the verb and quoi when it comes after. There are many exceptions, see your grammar books or Wiktionnaire for more detailed rules.

When the interrogative pronoun is the subject of the sentence, you can use qui if it stands for a person, but not if it stands for a thing. There is no neutral subject interrogative pronoun, you need to use “que’est-ce qui”. For example, “What did that to you?” = “Qu’est-ce qui t’a fait ça ?” As you can see, “qu’est-ce qui” is the translation of what when it’s the subject of the sentence.