Torque is the amount of rotational force your engine exerts on its crankshaft. Horsepower is the work being performed by your engine in a given time. This is Traction is how well the vehicle can put torque to the ground. Lets get into a more detailed picture of each...
Torque: Basically a force rotating an object on an axis. (twisting) Think of a bycicle. You pedal a bycicle with your feet. As your feet push down on the pedal, you move a lever that turns a shaft. Your foot is the force, the object is the pedal assembly, and the axis is the shaft that holds the pedals and sprockets to the frame of the bike. You can measure torque lb-ft. One pound foot is equivalent to one pound of pressure exerted on a 1 foot lever from the central axis. If you have a 6" lever, you will need two pounds of force to equate to 1 lb-ft. Likewise, it takes only 8 ounces (1/2 pound) exerted over a 2 foot long lever to create 1 lb-ft. In order to increase torque, you must lengthen the lever or add more pressure to the existing lever.
Horsepower:Is a measure of work being performed over a period of one minute. James Watts came up with this formula. 33,000 foot pounds (of torque) per minute equals 1 horsepower. A very easy equasion is this: Horsepower = torque x rpm / 5252.
Traction:This is the tire's ability to "grip" the pavement. As torque is increased (either higher torque output from the engine or from multiplying the current torque) the ability of the tire to "hold on to the surface" decreases. Torque is limited to the amount of traction that you get. An easy example would be winter road conditions. Your engine cannot apply maximum torque because the tires will spin. If you engage 4 wheel drive, then you split the available torque between 4 tires instead of two. Now, you can theoretically apply double the engines torque to the wheels because each tire is recieving the same amount of maximum torque before wheel spin. So, if we take this theory to the dragstrip, you see how traction helps. Without traction, you cannot utilize the maximum available torque during launch.
Now, lets apply these three units into an easy to understand example. Lets use a bycicle. Your feet are the pistons, the pedals are the crankshaft, and the sprockets are the gears in your transmission. First off, how much torque is our engine making at the crankshaft? Well, I weigh 200 pounds. The pedal has a length of 6 inches. So, if I apply maximum pressure to my feet (cylinder pressure exerted on piston during power stroke) by standing on the pedal and the pedal (our crankshaft) is 6 inches long, then I would be creating 100lb-ft. Make sense? Now, say my drive sprocket is 15 teeth and the driven sprocket is 30 teeth. This equates to a 2:1 gear reduction. Now, I'm applying 200lb-ft but only turning the shaft half as fast.
How much horsepower is my bycicle making? Interesting... I know I'm creating 100lb-ft. I need to know how often I create 100lb-ft during one minute. Since I'm standing on the pedals, lets say I make one revolution every 2 seconds. This means, I'm spinning at 30rpm (revolution per minute). Lets get out that handy dandy formula mentioned earlier and start plugging some numbers. hp=tq*rpm/5252. hp=100*30/5252. This comes out to about 0.57hp. (whew, my legs are tired and thats all I could do!?)
Now, lets say I decide to venture out with my bycicle in the winter. I'm approaching a hill and need to apply maximum torque to get up it. But WAIT!!! there's ice. Normally, I was able to stand on my petals and make maximum torque to get up this hill without any problems with the back tire spinning. But this time, my rear tire cannot hold. I apply half of my body weight to the pedals (only creating 50lb-ft) and the tire spins. This means, I can only make 50lb-ft and no more.
The reason people say torque is what gets a car going and hp keeps it going is because of this...
Back to the bycicle example. I was making 100lb-ft of torque. Pretty good for a machine that weighs 250lbs. But, I could only create it 30 times in one minute. So, I start from a dead stop and push on the pedals to get it moving. My drive sprocket is 15 and my driven sprocket is 30. This means I have a 2:1 torque multiplication. Here we go... Starting to go pretty fast, but then I approach 30rpm and I'm going 10 miles an hour. Damn, I need to trade up some of that torque for some speed. I shift into a higher gear. Lets say this gear is a 1:1 drive. I can now go 20mph at 30rpm but I'm only exerting half the torque on the rear wheel as I was in 1st gear. So, I may not accelerate as fast but I'm going a hell of a lot faster than in first. This is torque.
Maybe I drink a redbull (those things claim to give ya superpowers). I can now turn the pedals twice as fast!?. So, I don't need to shift until I hit 60rpm!!! I'm still creating 100lb-ft of torque but at an unbelievable rate of 60 times per minute. I can now accelerate hard in first gear but I don't have to shift at 30rpm. I can now go 20mph in first gear where as I needed to shift into second to do so before. This is horsepower taking over.
Now you hopefully understand the basics of the big three. You can clearly see how each relate to one another. You only need enough traction to hold your vehicle's maximum torque. Anything more and you're wasting money. Anything less and you compromise available torque. Horsepower relies on torque and time. And torque relies on traction. Damn, not to bad for an "off the top o' the head" explanation. If you would like, I can go into more detail on how this works specifially. Such as gearing and power curves and such.