Hero fragments are tokens that once you have the required amount you will be able to trade them in for a hero to add to your collection. Hero fragments are items that can be obtained from Daily Challenge event reward chests (Level 2 rewards) and potentially other reward drops. It is also possible to buy them using hero tokens from the Token Shop (in the heroes Hall Building).
The downside to hero fragments is that you have to collect a lot of them for each hero, to get a purple hero you will need 150 and for an orange hero 200. The other problem with hero fragments is that each fragment that you get will be dropped for a specific hero which means you cannot apply them to a hero of your choice and you could end up mainly collecting hero fragments of heros you already have.
You can always see how many hero fragments you have collected by tapping the Hero button on the bottom right of the main screen and selecting the 'Fragments' tab.