A rhetorical question is a question asked for effect rather than for information. The speaker does not expect an answer, because the answer is meant to feel so obvious that supplying it would be redundant — and because an audience that answers silently has agreed with you more firmly than one that was simply told.
That is the whole of its power. The listener does the concluding, and a conclusion you reach yourself is harder to abandon than one handed to you.
Patrick Henry, arguing for war in 1775: “Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?” He does not pause for a reply. The question is shaped so that only one answer is available, and the audience arrives at it a half-second before he would have said it.
Closely related to hypophora, which poses a question and then answers it aloud. The rhetorical question leaves the answer to the audience; hypophora takes it back.
Becomes Loaded Question when it smuggles in an unproven assumption.
The rhetorical question is the most common device in persuasive writing and the one most likely to go wrong, because the mechanism that makes it effective is the same one that makes it dangerous. It works by making the listener complete the argument. If the step they are asked to complete is genuinely obvious, the device is doing honest work. If it is not, the question has quietly moved an unproven claim past them while they were busy agreeing.
The distinction is worth holding onto. “How much longer can we ignore this?” assumes the thing is being ignored and that it should not be. Both might be true, but neither was argued; they arrived inside the grammar of a question, where claims are not normally inspected.
In writing, the device also has a practical weakness: it cannot be re-read the way it was first read. A listener hears a rhetorical question once and moves on, but a reader can stop, consider the question literally, and answer it differently from the way the writer intended. A rhetorical question that survives a hostile literal answer is a good one. Most do not.