That well-worn expression means, "you've only seen a small part of the whole thing." When taken literally, it refers to an important aspect of icebergs: only a small part of the berg is visible above the surface of the water. The exact amount visible varies from 1/6 to 1/9 of the whole iceberg [source: Stone].
To figure out why, let's take a look at buoyancy. The buoyancy(upward force) exerted on an object in a fluid is equal to the weight of the volume of fluid displaced by the object. Here's an example using made-up numbers (which don't represent any real iceberg). Imagine an iceberg that weighs 100,000 pounds. Now drop your imaginary iceberg into the water. It will sink until it displaces an amount of water that weighs the same as the iceberg itself weighs. Because the iceberg is less dense than the water, a volume of water that weighs 100,000 pounds is less than the volume of the iceberg. The difference is the amount of iceberg that remains floating above water.
Why does the exact amount seen above water vary? Icebergs are usually a little more dense than other ice because they've been compressed by tons of ice for hundreds or thousands of years. Their exact density varies from one iceberg to another. Also, remember that seawater is denser than freshwater -- variations in ocean salt content will affect the iceberg's buoyancy as well. Finally, the shape of icebergs plays a role, and they will often roll in the water as they melt.
Iceberg Life Cycle
The life of an iceberg begins thousands or even tens of thousands of years before it reaches the ocean. Glaciers build layer upon layer of ice; centuries of this compression along with infinitesimal movement toward the ocean create a particularly dense form of ice. It may appear blue instead of white because most of the air bubbles have been squeezed out of it.
Once it calves, an iceberg will usually live for three to six years. This period can be drastically shortened if the iceberg floats into warmer waters. During the course of its life, waves batter the iceberg and smash it into land or other icebergs. Frequent thaw/melt cycles (both seasonal and daily) open huge crevasses within the iceberg. A complex internal structure develops. Some icebergs simply melt away to nothing.
Some bergs don't go out so quietly. An expedition sponsored by National Geographic encountered the cataclysmic end of one large iceberg, reached during the peak of the nightly freeze cycle at a point when the destabilized internal structure could no longer support the iceberg's weight. Dr. Gregory Stone, a member of the expedition, described the incident in his book, "Ice Island":
"The enormous iceberg …heaved upwards, one end pausing high in the air like the bow of a foundering ship, then crashed down, creating waves that swept through all of Hallett Bay and rocked our boat…[it] rose one last time and seemed to explode into millions of pieces like shards of crystal, covering two square miles of ocean. Later, we circled the debris field of shattered ice." [source: Stone]
A small percentage of icebergs never stray into warmer waters and may float in the icy Arctic for 50 years or more.