In the Fiendex (found at the bottom right corner of the main game screen), if you tap on a Fiend to go to their info page, you will see the amount of Meteormites needed to grow them to the next level.
For example, it might cost 1250 Yellow Mites and 10 Blue Mites for Temper to go from level 5 to level 6.
If you have less than this amount of Meteormites, you have the option to make up for this by using Diamonds to complete the process. In this case, the game asks if you would like to "Get missing Meteormites?".
In the next window, the game shows you how many Meteormites are missing and how many Diamonds it will cost to get the missing Meteormites. The cost of growing the Fiend is the same. The Diamonds are just a way to get there faster, without having to wait to have enough Meteormites. This will use up all of your Meteormites, plus the Diamonds needed to complete the upgrade.