A fire tear is a tiny spark of a fire known as The Fire Eternal. It acts as the dragon's soul, essence, or life force. If they shed their fire tear it means they are mourning (or, as it is said in Dark Fire about the last 12 dragons, a dragon can shed their tear willingly) and they will return to the clay (Gaia) unless something stops it from landing on the ground. David Rain and his special writing dragon Gadzooks experience this in The Fire Within, because Gadzooks is sad since David didn't love him then, and many questions are answered.