It’s basically a hybrid question and exclamation mark. I think it would be very useful for writing dialogue; but, after being invented in the 1960s, it has (alas) fallen out of favour. More info here.
Nonetheless, I did once sneak an interrobang into a manuscript to see whether anyone noticed… (Nope!)
Anyway, I was just now out to dinner and came across the following stuck to a wall:
The Wheeler Centre is a reputable Melbourne writers centre. This event appears to be a bunch of panelists dealing with philosophical questions. Not that I care much. I just love the fact it’s bringing back the interrobang!
Example sentence using interrobang: “How the F%^K do you type an interrobang‽”
(Answer: On a Mac, find it in the punctuation section of the “characters” menu (control-command-spacebar) and make it a favourite. On a PC, key in ALT 8253.)