The Nexus Crystal is the relay tool between your dragons and Mystical Creatures servers; they need this crystal to survive and thrive in our world.
Forgetting to update to the latest version of the Nexus Crystal may cause issues like eggs not hatching, they will not grow or breed. So, it's very important you keep up to date rezzing the latest version of it at every place you have one or more dragons.
The Nexus Crystal also allows you to setup all behaviors of your new baby dragons, like text, sounds, animations, movement range and breathing.
The Nexus Weaver is the current version of it, the one on the picture above, if that isn't the appearance of your Nexus Crystal pick up a new one at any Mystical Creature store.