In a nutshell, crystals are consumable items that players place on their weapons and armor. Unequipping them and/or dying may destroy said crystals, and this mechanic is presumably based -- at least in part -- on random number generation. Basic crystals grant increases to HP or MP, while rarer crystals only activate under certain conditions (but provide a much larger bonus).
The article also mentions the three tiers of TERA bosses and how crystals affect them, as well as a few example crystals and their effects. Read all about it on the official website.