To get into Dragon's Mouth Cave, you have to be fire or ice, as far as I know. For ice, it is boring and all that you do is collect fire, but for fire, it is wicked awesome, only because YOU SEE MALISTARE HIMSELF IN PERSON. For how it looks, well, it looks like a dragon's mouth. It's nothing to be crying over if you don't get in, though, because you are in there for about five seconds unless you read messages REALLY slowly.
Tinu in Krokotopia (he is the mander who greets you when you first arrive from the Spiral Gate) has a quest shortly after you arrive there that asks for a fire gem for a necklace he is making. This quest eventually sends you into the Dragon Mouth cave.