The torque converter allows the engine to spin independently of the transmission. If the engine turns slowly, like when the car is idling at a stoplight, the amount of torque that passes through the torque converter is very small, so keeping the vehicle from moving only requires light pressure on the brake pedal.

If you stepped on the gas pedal while the vehicle was stopped, you would have to push the brake harder to keep the car from moving. That's because when you step on the gas, the engine speeds up and pumps more fluid into the torque converter, causing more torque to be transmitted to the wheels.

Not only does the torque converter allow your vehicle to come to a complete stop without stalling the engine, it actually gives your car more torque when you accelerate out of a stop. Today's torque converters can multiply the torque of the engine by two to three times, which 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, the transmission would move at exactly the same speed as the engine, because this difference in speed wastes power. That's why vehicles with automatic transmissions don't get the gas mileage of vehicles with manual transmissions.

Some vehicles have a torque converter with a lockup clutch. When the two halves of the torque converter get up to speed, the clutch locks them together, which prevents slippage and improves efficiency.

Watch this short video from Allison Transmission to see how it all fits together:
Torque converter video clip