This is a good topic, it's been discussed on every automotive message board in existence and now I guess it's our time to flesh it out. So here's my thoughts...
First of all, the definitions of torque and horsepower given above are very accurate. But to add just a bit here, think of torque as Energy (rotational energy). Energy is defined as force x distance here, such as the 50 lbs of force applied to a 2ft lever arm in the earlier example. Further, think of horsepower as Power, which for this discussion is energy x time. 1 horsepower is equal to 550 lb/ft of torque per second, or simply "torque over time".
The most important thing in this discussion is examining why horsepower is the single most important factor to a vehicle's accelerative ability (or more truly, the vehicle weight to horsepower output ratio), yet has no direct application to the physics of acceleration. To understand this, you must first understand what makes a car accelerate.
Acceleration is a time based event, but the force (energy) behind it is NOT. The energy of acceleration is not just torque either, it's effective torque to the wheels, which is found by multiplying engine torque at a specific RPM by the gear ratio you are in and the final drive ratio (shown here in this example)....
Example A:
first gear transmission ratio: 3.42:1
final drive ratio (differential reduction): 4.27:1
engine torque at 5000 RPM: 150 lb/ft
150 x 3.42 x 4.27 = 2190.5 lb/ft effective torque
So in that example, our meager torque output is greatly magnified to about 14.6 times it's original amount of energy. Just as the 2ft lever arm in the earlier example multiplied the force input by 2, the gear reduction here multiplied the torque output by 14.6. Now if you know gearing, you also know that the final drive ratio is fixed for a given differential, but the higher the gear you select, the lower (numercially speaking) the transmission gearing becomes. This is why acceleration always feels weaker in the next higher gear; torque multiplication through gearing is reduced, thus reducing the energy available to accelerate the car.
So why is any of this important? Because, if you understand how important gearing is to the equation, you understand why torque output, taken by itself, is meaningless in estimating accelerative ability. A typical deisel engine in a car outputs near to (or over) 300 lb/ft of torque, yet is almost never as fast as gasoline engines making 100 lb/ft less torque at peak. This is because deisel engines cannot run at high RPM, and therefore cannot take full advantage of torque multiplication through gearing. Since most cars are geared to redline at similar speeds in a given gear (usually around 35-40 mph in first, 60-70 in second, etc...), the engine's redline and power output at high RPM are actually indicative of it's gearing. So let's say we have two engines, Engine A makes 300 lb/ft of torque at all RPM and 300hp at redline, while Engine B makes 150 lb/ft of torque at all RPM and 300hp at peak. Given the earlier math that hp = torque x 5252/ RPM, one can see that engine B must be turning twice the RPM as Engine A to make the same amount of horsepower with only half as much torque to work with. And this is extremely important to realize because, if Engine B's drivetrain is geared exactly twice as short (numerically higher), the effective torque to the wheels will be precisely the same at any speed relative to the Engine A drivetrain. Which means that, given the vehicles weigh the same and we throw out variables like drag and traction, they will both have EXACTLY the same accelerative energy available to move the car forward. Which means they will both accelerate at exactly the same rate, even though the first motor makes twice the energy of the second.
And this is why cars like the S2000, what with it's meager torque output, can run side by side a car of around the same horsepower but with much more torque. To state this simply, horsepower ratings are like a clean summed up guesstimate of a car's accelerative ability, because they nicely package in torque and gearing into one number. And while this is sligthly oversimplified (given I only have so much room to type), that really is how it works. Look at any two cars with about the same horsepower output and you will see they both have about the same acceleration curves... regardless of torque output. Although the S2000 only has about 150 lb/ft of torque to work with at peak, it's gearing makes full use of this torque to motivate the car. Which is why it still feels quick at 4000 RPM, when it's a full 3500 RPM away from it's torque peak.
So to sum up, torque is the only thing an engine produces. It is the direct measure of instantaneous energy the engine makes to provide acceleration, and is the only thing directly important to the physics of acceleration. And yet it is also the most useless single number to look at when judging accelerative ability of a car, since 1000 lb/ft of torque means nothing unless you've got gear multiplication (read: RPM ability) behind it.
Conversely, horsepower output is a direct derivative of torque, and has no direct bearing or application to the physics behind acceleration. Yet it is the single most important number in judging the accelerative ability of a vehicle, because it so nicely packages torque output, RPM ability and gearing into one roundabout number.
And this strange dichotomy is the reason why manufacturers always give both figures, and why people will continue to post excellently informative threads like this on every atuomotive message board across the world. So after reading this, all I hope is that you come away with a newfound respect for both horsepower and torque numbers, and do not immediately dismiss any engine for focusing upon healthy production of one over the other. After all, everything has it's application, the S2000 motor is a gem because it packages 240hp into a 320 lb engine/transmission combo, while the BMW 3.2L I6 weighs much more but has a wonderfully broad and muscular torque curve. Hope this helps explain things, peace.
Ps-As one last thing, I want to say that increasing torque output over a large RPM range continues to be the most effective way to increase a vehicle's accelerative ability. You can increase horsepower output without chaning maximum or even average torque levels (by moving the powerband to a higher RPM range), but this will never be as effective in cost or extra speed as simply making more torque. And that's because you have to adjust gearing to take advantage of this newfound RPM potential, which isn't cheap. This is why forced induction setups are so effective at improving acceleration with minimal cash outlays, and why making an NA car go as fast will take MUCH more time, effort and money to acheive.