Function Generator Sync Output Elementary Question

Both? As a trigger for an oscilloscope for example.

You could also use it to start a delay that, when it expires, enables something that you want to happen at the same time as a later portion of the waveform. Say you have a triangle wave and the sync pulse occurs at the start of the triangle, but your gadget needs to work at the peak of the wave. So you set the delay time equal to the time that it takes to get from the start to to peak. Now this sort of thing can be done on o'scopes with all the fancy controls they have, but suppose you only have the FG and your gadget? You could use a scope to set it up and then, when it's working, pull out the scope for another use, leaving the circuit working.

Or the above delay, triggered off by a single repetition of the waveform's synch pulse, could, after any amount of time, trigger off the FG! Thus one pulse fires the delay (yielding a second, minute, hour, day, week, month, year or whatever), after which another pulse is generated. Can your FG, as it stands, give one pulse per year? Of course it's a bit tedious experimentally setting the delay time just right. :-)