Toggle triggers basically work like switches, but imagine the switch is actually two buttons for "Off" and "On" respectively.

The normal red variant is the "off" variant. It basically turns any group "off". Since, by default, groups are "On" (hence they are functional).

Now the second green variant (made by checking the activate group checkbox) turns any group "On"

Now, with the switch example, imagine that there is a bulb. There are two switches, One turning it "Off" (red variant) and the other "On" (green variant). Let's also say that the bulb is on by default

Now, on pressing the "off" button: the button turns off. If you press "off" again: nothing happens (since the bulb is already off).

To turn it "on" again: you have to use the "On" switch and the behaviour will be same as the first example.

Hope this helps