Most drivers are familiar with the term horsepower as it applies to automobiles. More horsepower equals a more powerful engine. More specifically, a horsepower is defined as 550 foot-pounds per second which means the equivalent of the energy required to push 550 pounds over a distance of one foot in one second. That figure is equal to moving 1 pound 550 feet in one second, 225 pounds over two feet and any combination that works out to the same total.
In terms of your car, the horsepower is the total amount of power available to make the car go. Since the car's weight is constant, notwithstanding cargo and passengers, more horsepower allows it to cover more distance in fixed period of time. In other words, it'll go faster.
If power is determined by horsepower, what does torque have to do with anything? Torque measures the amount of force applied to twist the crankshaft. At a given horsepower, a low torque engine spins the crankshaft faster with less twisting force while a high torque engine would spin it slower with more muscle behind it. From there, the transmission gearing determines how fast the car moves in response to each revolution of the crankshaft. With the right transmission, either can achieve the same overall vehicle speed.
So what's the difference? The difference is that to produce the same total power, a low torque engine by definition must be running at higher RPMs. From idle, it may take longer to rev it up to speed in order to get maximum power applied to the crankshaft and eventually to the wheels. The higher torque engine may feel more powerful simply because the car responds faster to the accelerator even though both may have the exact same maximum speed.
Torque is related to the amount of engine's displacement (the volume of air pushed out by each stroke of the piston cylinders. Bigger engines, therefore, tend to provide higher torque.
What does that mean for the everyday driver? For a smaller, lighter car, it takes less torque to get the thing rolling and a smaller, lower torque engine that runs at a higher RPM is fine. High torque is a less important for these vehicles, unless you want it to really jump off the line.
For a heavier vehicle, more torque is required to start all that weight moving, especially if you're towing or carrying a heavy payload. A lower torque engine would make it seem fairly sluggish as you waited for the RPMs to get high enough to provide the needed rotational power to the crankshaft. For these vehicles, higher torque engines provide crankshaft power sooner without revving the engines up to extremely high RPMs.