The portability of Gemstones
The diamond industry is famous for being a transferrable source of portable wealth. It is very difficult for customs agents to discern a million dollar ring on the finger of a traveller and using this method billions of dollars circulates through the worlds airports in a manner that would be impossible if it was ‘suitcases full of cash’. Diamonds are very much a means of cash transfer ‘under the radar’.
There are many, many reasons why people smuggle diamonds yet they all have to with the "density of value" of diamonds which is unsurpassed by even gold or platinum. Here is a 22 million dollar 100 carat diamond recently auctioned off by sotheby's.cnn.com/2015/04/20/world/sothebys-flawless-diamond-25-million/ As you can see it is small and light enough to be carried on a person's finger and can be easily concealed from authorities. $25,000,000 worth of gold however would be extremely heavy to transport and also much harder to conceal.demonocracy.info/infographics/world/gold/gold.html
And this site has an illustration of what 80 million dollars would look like! trends.jewelry/worlds-most-expensive-jewelry/
As you can see, diamonds are a good way to carry a lot of money, in a small concealable package! I think that if you simply walked through customs wearing a diamond necklace they wouldn't even bat an eye as they would most probably assume it was fake.
So now that we know that diamonds are an excellent way to compact a huge ammount of money into a small space - we can answer your question as to why someone would want to smuggle them. The reasons are varied but always nefarious and the shenanigans usually start the moment the diamond leaves the ground. The poor lowly miner might want to supplement his meager wages; by smuggling diamonds out of the mine on his person, for resale in the black market. Or it might be the mine manager smuggling out the diamonds from the mill on behalf of the company to avoid paying royalties as is rumoured to happen in Canada. It could be perhaps that a wealthy "businessman" would like to transport his wealth out of a country without paying the appropriate taxes. Because diamonds (especially uncut) are nearly impossible to trace back to their source - it might be to smuggle them out of a "blood diamond" sanctioned country - to be mixed in with a parcel of legitimate diamonds from a legitimate countries package. Or they might be smuggled into a country to pay for drugs, or arms, or to be used in a money laundering scheme. economist.com/node/1034471
Whenever undeclared diamonds are being transported across a border you can be sure that there is a criminal reason for it and that is why there are blanket laws to prevent people from doing just that. Enforcement of those laws is another matter - but you can be sure that wherever you find diamonds - the crooks will be right there too. narrative.ly/confessions-of-a-jewel-mule-that-time-i-smuggled-a-fortune-in-precious-gems-through-us-customs/
This is a great article that gives valuable isight to this problem: