Good question! I think the key benefits of blockchain technology include the tamper-free nature of the data and the ability to form consensus, thus, for the diamond trade, you can provide an audit trail for each stone.
It becomes increasingly effective as more people make use of the platform. Image a scenario: a stone is cut, certified and sold; all of its properties recorded in a blockchain. At some point, the stone is sold by a dealer, which is again recorded. At some point in the future, the customer is burgled and reports the stone missing. Once again, this is recorded in the blockchain. Now at any point in the future, if the stone falls into the possession of another dealer (i.e. somebody attempts to sell the stone), or if it is recovered by the police, they will see immediately that the stone was stolen.
There’s an interesting article on this very topic, if you’re interested: http://techcrunch.com/2015/06/29/everledger/
Sorry — just realised I didn’t actually answer your question. Dealers wouldn’t need to understand the underlying technology; like with most things, the complexities would be abstracted away behind a user interface of some description and interact with system that way. Much like how it’s not necessary to understand how blockchain works in order to buy/sell Bitcoin.