Tech shards are used to forge wargear (which can be equipped by heroes) and relics (which can be placed on relic pedestals). They come in 3 strengths (lesser, greater and flawless). Lesser shards usually produce common wargear/relics but sometimes produce uncommon ones. Greater shards usually produce uncommon equipment but sometimes rare ones. Flawless shards usually produce rare equipment but sometimes epic ones.
When should you forge relics and when should you forge wargear? First, lesser and greater shards should always be used to forge wargear. Here are a few reasons why:
There will come a point when you have good offensive relics with each of the 4 key categories mentioned in the Offensive Relics section. At that point, you may want to start forging wargear with your flawless shards.
But even still, forging relics is still valuable as you might get even better bonuses. Also, if you can get relics with two or more great bonuses on the same relic, you can get both bonuses using only 1 relic pedestal. There are 8 potential bonuses for offense, but you can only deploy 5 relic pedestals, even with a maxed out forge. So relics with 2 or more great bonuses are invaluable.
Tip: Flawless shards may produce epic wargear. If you don't have an epic hero, you won't have any hero to equip epic wargear on, so it will either take up a wargear slot unnecessarily, or you will sell it. In that case, it would have been better for you to forge an epic relic. For this reason, flawless shards should generally be forged into relics for the most part. Especially if you don't have any epic heroes.