CITES stands for the Convention on International Trade in Endangered Species. It's not an international law or anything, however if a country becomes a member of CITES, then they are required to follow CITES rules. Some of the important CITES countries are Indonesia (why you couldn't get a frogspawn- they were renewing permits) and Fiji. Some of the countries that aren't with CITES are Solomon Islands and Tonga. The Philippines is a member, but have a self imposed ban on CITES species.
So what does CITES control? Well, for our trade they deal primarily with Appendix II hard corals, live rock, and clams. (Appendix II listings are legal to collect & export, but the trade is monitored.) Live Rock, listed as Scleractinia, also comes into play for animals like soft corals, mushrooms, polyps, etc... they are attached to it. Although a leather coral, green mushroom, or button polyp is not a CITES animal, the rock they grow on is, so you must have a permit for the rock.
The country of origin issues a CITES permit which must accompany your shipment. Fish & Wildlife then makes sure that your CITES permit matches your invoice. For example, say I have a really short CITES permit that lists the following:
10 Euphyllia
10 Trachyphyllia
20 Scleractinia (the designation for live rock)
I can legally import the exact numbers that are listed on my CITES permit. If my invoice shows 11 Euphyllia, I'm going to get one confiscated by F&W. Or if F&W does a random inspection on my shipment and finds 10 Turbinaria, all 10 will get confiscated.
If you have any other questions, just ask!