Once the voltage across the DIAC exceeds 32V, it will turn on, basically acting like a regular forward biased diode, with the current limited by the resistance in the circuit that delivers power. If the power source can only supply a limited current, the DIAC will stay on till the current drops below the holding current, and then turn off again. Thus you typically use a DIAC where you charge a capacitor up to a higher voltage than the breakdown voltage, and discharge it through the DIAC, with the current that flows through the DIAC and the load being limited to some current pulse below the maximum rated current. The resistance that charges the capacitor must be high enough that the current flow when the capacitor is fully discharged is below the holding current, and thus the DIAC turns off, and the capacitor starts to charge again.
In AC use the same, just that you typically want to get the current pulse some time after the mains zero crossing, so the resistor allows the DIAC to charge up on each half of the mains cycle, and then discharge the capacitor typically to turn on a bigger thyristor or TRIC, which then keeps the voltage across the DIAC low for the rest of the mains cycle, so it only generates a single delayed pulse per half cycle of the AC voltage. next half cycle the thyristor or TRIAC turns off at the zero crossing point of the current, and then the voltage across the resistor limiting the charge current into the capacitor allows it to slowly charge to the breakdown voltage of the DIAC again, turning it on, and thus the thyristor or TRIAC, for the remainder of that half cycle.
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