The answer to a "¿De qué...?" is a noun or noun phrase preceded by the preposition "de", and the answer to a "¿Qué...?" question is not preceded by the preposition "de".
Intuitively, "¿Qué...?" means "What...?" and "¿De qué...?" means "About what...?" or "Of what...?" or "From what...?". However, in English the preposition in questions usually comes at the end, so "¿De qué...?" is usually "What ... about?" or "What ... of?" or "What ... from?".
Examples
¿Qué tienes ahí? -- Mis llaves.
What do you have there? -- My keys.
¿De qué estás hablando? -- (Estoy hablando) de tu trabajo
What are you talking about? -- (I am talking about) Your work.
¿De qué tienes miedo? -- (Tendo miedo) de su reacción
What are you afraid of? -- (I am afraid of) her reaction.
Note how the answer to "¿De qué...?" has "de" before the actual noun or noun phrase that answers the question. The intuitive check that the English translation of the question has a preposition at the end may not always work, as there may be verbs that require the preposition de in Spanish but require no preposition in English. An example of this is "olvidarse de algo" (forget something):