Tons of misinformation here. As we know from ohm's law, power (watts) = Current (amps) X Pressure (volts). Impedance is a restriction to the flow of AC current. When you lower the impedance, you cause the speaker to draw more current to reach the same power level. Going back to Ohm's law, you can see that when you increase the current flow, you also lower the voltage delivery because less pressure is required to deliver the power. More current, lower voltage and vice versa. Increasing the current draw from the speaker also increases the heat generated by the amplifier because amplifiers aren't 100% efficient. The amplifier has a thermal sensing circuit that shuts it down when the temperature hits a dangerous point because excessive heat can damage the amplifier circuitry. So what low impedances do is cause the amplifier to run hotter for the same power as a higher impedance. That's the whole issue.
How hot the amplifier runs depends on many factors - the major ones being the current draw we described above, the sound pressure level at which we listen and ventilation. Impedance ratings for amplifiers are based on full power output. Understand that we rarely if ever use our amplifiers at full power. My home theater will play quite loudly with an average power consumption of 1 watt average and 10 watts or so on peaks. Just check the sensitivity of your speakers and you can work out the math very easily. Sensitivity rates the db of sound pressure with 1 watt of power at 1 meter. Then moving away from the speaker, the sound pressure level decreases by 3 db for each doubling of the distance. So most of us are running somewhere between 1/2 a watt to 3 watts on average with our hundred watt amplifier in a normal room.
Impedance ratings for amplifiers are based on full output power.. Although it isn't that simple, amplifier X is rated to deliver 100 watts into 8 ohms. If we keep the voltage the same, that same amplifier will deliver somewhere near twice the power into 4 ohms but we stand a chance of overheating the amp if we run full output power long enough to heat up the circuitry. As we know, however, we don't keep the voltage the same. It reduces as the current flow increases to keep the same amount of power. But if we run the same amp at, say 50 watts or 1/2 of its rated power, then the current flow is reduced by about 1/2 and the thermal emergency is over. If we run the amp at 1 watt, it has little problem at all with the speaker impedance. In other words we could take the same amp that is rated for 100 watts into 8 ohms and rate it at 50 watts into 4 ohms. Now everybody is happy. We now have a 50 watt amplifier which is still way bigger than we need, rated at 4 ohms.
If you followed all that, it attempts to explain why audio consumers are hung up on speaker impedance but probably should not be. The reality is that speaker impedance is not constant. It varies by frequency and it varies a lot. The nominal impedance rating that manufacturers put on speakers is an attempt to guide the consumer in mating an amp to a speaker. Actually it only describes the impedance curve at a few points along the frequency spectrum. You can view it as an average even though it isn't an average. If we were using 5 watt amplifiers those nominal impedance ratings would be critical. Since we're using 100 amplifiers, they aren't so critical. Our 100 watt, 8 ohm rated amplifier will probably deal just fine with 2 ohm impedance dips in the curve as long as we don't turn the volume up too high or hit 2 ohms for a significant amount of time.
Consumers, for some reason, are concerned about amplifier power, not speaker impedance so amplifier manufacturers rate their power output for continuous duty into 8 ohms (about as high as speaker impedances get in practice) because that makes the power number higher. Speaker manufacturers then have a tendency to rate nominal impedance as high as they can get away with so that the consumer won't worry about the impedance that he shouldn't really worry about in the first place. Any amplifier rated at 8 ohms is also rated at 4 ohms at a lower power output level and 2 ohms at an even lower one. It is a numbers game. The reality is that it would be stupid for a speaker manufacturer to make speakers that would cook the average home amplifier and it would be equally stupid for an amp manufacturer to make a product that couldn't survive driving all those available speakers out there. They aren't stupid.
The average consumer knows nothing of Ohm's law or speaker impedance. He just goes to a store and buys what he likes and hooks it up and enjoys the audio. If there were actually a good chance that he would burn up his amplifier, we would hear stories about cooked amplifiers all over the place and we don't. The only ones I've seen involve abuse like wiring a dead short across speaker output terminals and things of that nature. Quit worrying about speaker impedance. For the vast majority of us, it simply isn't an issue. If we listen in an auditorium where we will stress the amplifier's capabilities, then it can be a problem but few of us listen in an auditorium. Hope this helps clarify a few things. If I wasn't clear somewhere, let me know and I'll correct it.