When you finish crafting a new sword, you are giving the option to save it. When you do so, bit by bit, you are building up and completing collections.
A collection is completed when you have crafted and saved every single type of sword you can make from a material. When you have completed a materials collection, you are given with a Divine Metal as a reward.
Some collections are easy to complete, e.g. Copper. Others will take you months and months to complete, such as Sacred Stone and Demon Stone. Divine Metal will only be completed after a very long time of playing, and possibly buying Smith Tokens, though due to the fact that your drops are guaranteed, it is possible you could complete your divine metal collection before you complete your sacred stone one. Gold & Diamond share a collection page.
1 very important thing to remember is that you can not save a sword you have never completed, so do not try to trade for swords you have not crafted just to increase your collection.
As you will notice from the below chart, you get a lot of Divine Metals. The current count for items you get, upon completion are: