Benefits and Weak Points
In addition to the very important job of allowing your car come to a complete stop without stalling the engine, the torque converter actually gives your car more torque when you accelerate out of a stop. Modern torque converters can multiply the torque of the engine by two to three times. This effect only happens when the engine is turning much faster than the transmission.
At higher speeds, the transmission catches up to the engine, eventually moving at almost the same speed. Ideally, though, the transmission would move at exactly the same speed as the engine, because this difference in speed wastes power. This is part of the reason why cars with automatic transmissions get worse gas mileage than cars with manual transmissions.
To counter this effect, some cars have a torque converter with a lockup clutch. When the two halves of the torque converter get up to speed, this clutch locks them together, eliminating the slippage and improving efficiency.
For more information on torque converters and related topics, check out the links below.