While the basic concept was answered pretty well in the second post,
http://www.arboristsite.com/chainsaw/123923.htm#post2000406
...no one seems to have explained why they used gear drive. Modern saws are quite effective with chains that travel at high speed. They get this effectiveness by using very high revolution speed. So a 5 hp motor at 12,000 rpm can take MANY tiny bites of wood and cut very effectively.
Switch to an old fashioned saw at 5hp. The engine RPM is only about 4k, so your chain is going to turn pretty slowly. This means that chips will not clear the groove as well as modern saws, it means that even a slightly dull saw will not pull easily through the wood, and it means that you must FORCE the chain through the wood.
Much like it takes tons of raw force to push a nail into a 4x4, a one pound hammer can do the job pretty well with fast light blows. The physics are not much different for saw chain in wood: slow it down and the force required goes up exponentially. This additional force requires a big heavy chain to survive, and mandates larger contact surface at the sprocket to deliver the torque required.
So the engineers went to work: they could put somewhat bigger diameter sprockets on the big chain drive to capture the bigger forces applied by the wood against the chain; but this reduced the ability of the engine to pull the load. A bigger diameter sprocket means reduced torque delivered to the chain.
How to correct this problem? Gear reduction ! This drives the chain with MUCH more force and relieves the clutch from having to deliver all that torque, too.
Since the chain is being forced through the wood, rather than slicing through quickly, you will also see that the older chains were all "chipper" tooth, rather than semi-chipper or square toothed, like we see today. I won't even go into the older styles of cutters that have fallen by the wayside.
Obviously, all that "bigger, heavier, stronger" stuff makes for a damned heavy saw, so the manufacturers have been working on "lighter and faster" for at least 40 years.