The capacitor in a disposable camera fills up with power from the battery. It is then used to very quickly pulse the stored energy through the xenon flash tube bulb. The capacitor is capable of discharging all of it's energy almost instantly. A battery on the other hand can only discharge it's power slowly by comparison. So for the high power flash, we use a capacitor to give it that large jolt of power to produce the very bright flash. The "slow" battery then takes it's time (a few seconds) to recharge the capacitor for the next picture.
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