Speedmaster,
A persistent caprifig will produce "ripe" figs even if it is not pollinated by the fig wasp (think of it as a common caprifig: persistent = common).
A non-persistent caprifig will produce NO "ripe" figs, UNLESS it's pollinated by the fig wasp (think of it as a smyrna caprifig: non-persistent = smyrna).
It's important to find out if it is persistent or non-persistent because the persistence gene is only carried by the caprifig, NOT THE FEMALE FIG. Therefore, a non-persistent caprifig will have no persistent (common) offspring. Persistence (common fig) is important for every fig cultivator (the fig wasp is not around all the time to pollinate figs), but especially for those in areas without the fig wasp, who will need to grow common varieties in order to produce a crop.
Persistent Caprifig + Persistent Fig = 1/2 persistent offspring + 1/2 non-persistent offspring
Persistent Caprifig + Non-Persistent Fig = 1/2 persistent offspring + 1/2 non-persistent offspring
Non-Persistent Caprifig + Non-Persistent Fig OR Persistent Fig = 1/1 non-persistent offspring
Here is a very good online resource that explains all of this in great detail: http://waynesword.palomar.edu/arbimg10.htm#persistent
In a way, I'm happy I was never required to learn about "Ficus Culture" in high school biology. Saying it's complicated is an understatement. But I hope I helped to answer your question.