Sound is a funny thing. The loudness of a frequency - as we percieve it - is not related to its actual power at all, and it's not even directly related to the amount of power used.
SPL is a measure, quite literally, of the pressure a sound wave exerts - how loud it is. The unit of measure is the Bel - or, more commonly, the decibel, or 1/10 Bel. Louder sounds, of course, exert more pressure than softer sounds. However, SPL is not measured linearly - it's logarithmic.
Every time a signal increases in strength, it increases by 3 dB. To make your stereo 6 db louder requires a whopping four times as much power to the speakers - give or take. This also means that a seemingly small difference in efficiency - the amount of sound produced at a given amount of power, measured in dB at one watt at one meter - can make a huge difference: A 91db/w efficient speaker will produce 100db at one meter using eight watts of power, while an 82db/w speaker would require sixty-four watts - a substantial increase, indeed!
However, making your stereo twice is loud is not so simple as doubling the power to the speakers - human ears don't work that way. Instead, we percieve a doubling of loudness every time the signal strength is increased tenfold - or, in other words, a 10db increase.
This is very important for subwoofers and other highly inefficient speakers - in a stereo where only twenty watts go to each of the 91db/w efficient tweeters, the 84db/w subwoofer requires two hundred watts to keep up. This is also why seemingly tiny differences in loudness can mark the difference between a car stereo and an electrical substation.
Of course, distortion of almost all amplifiers is inherently lower at low frequencies, and subwoofer amplifiers - usually built-in as "plate amps" - can be of a much lower grade than the other amplifiers in the system without a decrease in sound quality. This is especially important for class-D amplifiers - while a high-grade class-D amp is fine for any application, lower-quality class-D amps' distortion can be awful at high frequencies, but is nearly unmeasurable at the low frequencies used with subwoofers.