The heroes will lose if any core is destroyed. They also get healed before a boss fight on all difficulty levels, on most maps. On Easy/Medium/Hard, all cores get fully healed after each wave. The crystal has a finite amount of health, depending on the map and difficulty set. On most maps, one or more Eternia Crystals have to be defended from enemy attacks. They banished an immortal evil called the 'old ones' inside Eternia Crystals and now their children must stop the hordes of enemies from unleashing the evil that resides within them.
The origin of the Eternia Crystal has to do with the parents of the four playable heroes.