Let's think of it with some values. We have a frequency of 50Hz. So, time period is 20ms. One half cycle is 10ms.
When you give 66%, it means that you want power on the device for 66% of the time. The remaining 34% should be off.
66% corresponds to 0.66 * 10ms = 6.6ms each half cycle. 34% corresponds to 3.4ms.
A triac is used as a power switch. When a triac is turned on, it stays latched on until the next zero crossing. So you can't just turn it on at the beginning of the cycle and turn it off after 6.6ms. The triac will just stay on for the entire 10ms, delivering power for 100% of the time. So what is done is that, at the beginning of the half-cycle, the required off time is waited. That is, for the required off time, the triac is kept off. The triac has not yet been fired. So, for 3.4ms, the triac stays off as it has never been fired that half-cycle. After 3.4ms the triac is turned on and it stays on for the remaining 6.6ms.
So, you're right. When you give 66% "command", the device is powered for 66% of the time.
Hope this helps.
Tahmid.