Rough Diamonds are objects that allow you to obtain a lot of GMP, which is a special currency in Metal Gear Solid V. A single diamond, depending on how large it is, can be worth 10000 or 100000 GMP. It is quite a lot, so you can largely increase the pace of Mother Base development or unlock the best inventions faster.
On the next pages of this game guide, you will find examples of locations where you can find diamonds in early stages of the game. Try to visit these places as soon as you can and collect the diamonds. This will make it easier for you to progress through the campaign. Later in the game, you can go back to these places (the diamonds appear again after some time) or find some other locations to collect the diamonds (for example in Africa).
Note - if you don't know where to look for diamonds or you have troubles locating one particular diamond, you can interrogate one of the enemies. There is a high chance that he will tell you the location of the diamond and it will be marked on your map.