OK, let me try to confuse things more. Max, and especially Min power doesn't make much sense for speakers.

Let's start with the "Min" power. There of course is no real "minimum" power for a speaker - you can actually play as quietly as you want without breaking the speaker and without it sounding bad. But there is a more important factor - efficiency. Some speakers require less power to produce a certain sound level, others more. And if you try to push an amp beyond it's rated *sine* power, it will distort. Distorsion not only sounds bad, but produces high frequency components that might blow your speakers.

So the amount of power you need from your amp depends on two things - how lound you want to go, and the speaker efficiency (measured in dB/watt - so X dB of sound per 1 watt of input). These together determine how many watts you need to deliver the required amount of sound (in dB).

As to the Max power, what you want to avoid is destroying your speakers. There are two major ways of destroying a speaker - mechanical and termal. If the speaker has to make movements that are just too large, something will break - the membrane rips, voice coil bottoms out and gets scraped, or whatever. And if you put too much electrical power into the voice coil, it gets too hot, and breaks.

Especially the mecanical limit depends on the frequency - low bass is most likely to break the speaker (depending on the resonant frequency of the speaker). So the max power limit reflects some idea of typical music power that won't break the speaker.

On a multi-element speaker (one with a separete tweeter), the power handling capability of the tweeter is usually much more limited than of the main/mid speaker, as there usually is much less energy in the upper frequencies. But if your amplifier clips and produces heavy distortion, it might produce enough energy in the high frequencies to blow out your tweeter even if you are within the power handling capability of the speaker system.

To make everything far more complicated, the enclosure and mounting of the speakers has a large effect on it's power handling (and even efficiency). Let's not go into that....

Confused? You will be even more confused after the next episode...