The Time Chasm Crystal Shards are late game items that unlock once you finish the main scenario, and kill Demigra. These items are used to unlock a whole extra scenario for you to battle through, and will unlock the Legendary Super Saiyan Saga.
Obtaining these rare items isn't as difficult as you might expect, as two of them are handed to you.
Once you have all five, return to Future Trunks. He will have a new mission for you. These new missions are actually part of the Legendary Super Saiyan Saga, the unlockable Saga that you need the Time Shards to obtain.
This Saga is very difficult, and is meant to be challenged with a high level character.