Most will be familiar with people quoting the power output of their cars, especially when standing at the bar. And of course you should realise that most of those figures quoted are likely to be exaggerated somewhat. That is of no great matter here, but do bear that in mind when hearing comments about the 'massive power increase' that is claimed for some modification or other; the claim is often not entirely correct...
There are two measurements relating to power outputs that are mostly of interest. The first is the peak level of power that an engine can produce. This is at it's optimum rev range, usually approaching the rev limit for an engine, since the more revolutions of the crankshaft means more firing strokes to create power. The other measurement is the amount of torque generated by an engine. This can be a bit harder to understand, or to explain, but it is essentially the amount of 'twisting force' put out by the engine. Power and torque are directly related at any particular engine speed, since two of the figures are multiplied together to get the third.
This means that a 'power curve' for an engine can be plotted to show the amount of power at each step in the rev range, and also the amount of torque generated. Higher peak power can mean a greater top speed for a car, assuming suitable gear ratios for the vehicle. However, increased torque throughout the rev range will lead to much better acceleration. A 'peaky' engine is one that has a high maximum power output, but only in a narrow rev range. This means that to make the best of the engine, the driver will need to work through the gears to keep the engine operating within this area of the power curve. A more 'torquey' engine has a wider spread of power and can pull over a wider range of engine revs. This leads to better driveability and frequently results in better acceleration times.
Power is a unit of work, measured in BHP (Brake Horse Power) - in pre-metric days, at least.
Torque is a measure of force, stated in lb/ft (pounds per foot), much as you would see on a torque wrench - since it measures
the same type of force, a twisting force equivalent to a certain weight or pressure (lbs) applied on a fixed length lever (1 foot).
Note that measurements used here mix Imperial terms (bhp, lb/ft) and metric measures (Nm, Kg) as these are more commonly encountered.