Torque is literally the turning force of the engine but in isolation the measurement is meaningless to determine acceleration. If you had 500Nm @ 5000 rpm you have a decent engine with which to power a car. However if you have 500Nm @ 1000 rpm you have a tractor engine and NOT a good engine for a car for acceleration. The reason is gearing. If you want to do 0-60 quickly (you could select any specific speed) you select gearing as low as you can to reach 60 in your chosen gear. If you have an engine that can apply 500Nm @ 5000 rpm you can aim to hit 60 @ 5000rpm. This means relatively low gearing. If you have the other engine you have to try to accelerate in a VASTLY higher gear hitting 60 @ 1000rpm. We all know acceleration is greater in lower gears. The torque is in fact multiplied by the gearing. Remember you legs don't get stronger when you change down gears on a bike, the gearing makes it easier to turn the crank.
What you want to go fast is the ability to run high rpms whilst sustaining the torque. Low down torque makes for relaxed cruising, good emissions and can aid acceleration
when you do not use the gears, BUT its not faster. This is why many diesel engines having LOADS of torque but modest power, are not faster than a petrol engine with lower max torque but more power.
Spread of power is important too and then you get into the specifics of the gearbox used. Type, number of gears, etc.
In summary power is the rate at which the engine can do work. It is the best single term to use to compare engines for acceleration. If you can adjust the gearing the engines of the same power will accelerate at the same rate. I have studied the science behind this.
If you want an example my 550BHP/ tonne Ariel Atom has bugger all torque but its high POWER to weight makes it one of the fastest accelerating cars on the road. Partly due to screaming to 8250rpm and running relatively low gears. But for long distances it would drive you mad.
