Dual supply isn't required, but it lets you output upto the two voltages.
An op amp's output is limited to what's called the saturation voltages, which is the two voltages you supply to it. For example, say you have an audio singal, which is AC, at maybe 4 volts peak to peak. You put this signal to an op amp configured to have a gain of 10, if you supply the opamp with +/-15v, when the audio signal gets to either +1.5v or -1.5v, the op amp will multiply that by 10 and reach it's saturation voltage. After this point, the op amp will only output +/-15v until the input voltage drops back below 1.5v and part of your signal will get cut off.
So, if you supplied the op amp with only +15 and your other voltage is 0, the op amp will only output 0 volts on the negative part of the audio signal. Or at least this is my understanding of it.