minime,
The triac will turn off by itself when the current waveform crosses zero. If you turn it on just after that, it will be on for a almost a full cycle. If you turn it on just before then, it will be almost off never on. Regardless, if you want smooth operation, you need to time your pulses in sync with the line voltage.
If you don't sync, say by drive with a PWM that has no relation to the AC line voltage, you will get odd, flickery operation. The turn on point will be driven by the PWM output going high, but the turn off point will still be driven by the line current. So you'll get a bunch of random 'runt' outputs, etc.
Random phase just means it will turn on whenever you say. ZC detection means the device cannot be used for dimming, it will only turn on for whole cycles.
PS -- if you were controlling a heating element or something else whose output only matters to you on the order of many cycles, then you could skip the ZC altogether and just slow your PWM down so that it operates over many cycles. But even then you'd probably want the ZC detecting opto-driver as the partial cycles are of no benefit to you and they cause noise.