Dragon caves are underground structures that house level 4+ dragons inside them.
Fire dragon caves are rare, underground, sphere-shaped structures made up of Charred Stone, Charred Cobblestone, and blocks of various vanilla Minecraft ores.
As of yet, there is no reliable way of locating a dragon cave in survival. The only way of finding one is digging and exploring underground and hope you get lucky. Dragon caves are incredibly sought after, as the only natural spawning place of wild stage 4+ dragons, of which the females drop Dragon Eggs. Around are piles of gold that are the dragons treasure.
Ice dragon caves are rare, underground, sphere-shaped structures made up of Frozen Stone, Frozen Cobblestone, and blocks of various vanilla Minecraft ores. Around are piles of silver that are the dragons treasure.
Dragon Caves are the only place where wild stage 4+ dragons can be found. Other than that, the caves do not spawn anything else. However, the natural darkness of these caves can lead to the spawning of hostile vanilla mobs.
Other than the loot of the slain dragon, the cave has other potentially valuable loot. The floor of the cave is usually covered in Gold or Silver Piles. There are also many chests throughout the cave, which can have various loot inside. See the Infoboxes for precise list.
For tips on taking on a dragon and getting your first egg, see Dragon Fighting Tips.