Current causes heating and heating can cause fires.
Think about a home lighting circuit. Lighting circuits operate at a constant voltage (perhaps 120V). Let's say that it is a 1500 Watt circuit. This means that the circuit can supply a certain amount of current without overheating. Fuses are used to prevent over current situations that might result in a fire. This implies that one could safely connect up to (15) 100W lamps on that circuit -- each lamp drawing 100W from the circuit.
Speaker circuits are different because the signal level (voltage) varies from instant to instant. At the zero Volume setting or silent music, there is no current and one could connect a thousand speakers without hurting the amplifier.
Amplifier and speaker ratings are very slippery because there are no universal standards about how to specify the limits. An amplifier limit might be rated at 100W when driving an 8-Ohm load. This same amplifier would be rated differently if operated into a 4-Ohm load -- or the amplifier may not operate at all on 4-Ohm loads.
Speaker ratings are very complex because the same voltage presented to a speaker will result in more or less current -- depending on the frequency. Typically, the speaker will draw more current at lower frequencies and there will be a peak somewhere below 100 Hz. And, the maximum safe current varies by frequency. If you presented the speaker with a maximum level 20KHz tone for more than a few seconds, the speaker's tweeter will probably fail.
The speaker ratings quoted in the advertising literature are simply recommended maximum and/or minimum amplifier power for average use. If you think that this is a weaselly way to specify things, you are correct. However, in defense, the lay public could not deal with a series of graphs that properly lay out the speakers capabilities. Typically, the marketing department determines the maximum power number assigned to the product, not the engineering department. I tend to believe the number specified for low grade products (10W or so), I don't believe the 200-400W ratings for low grade braggart type products. If you give me a job "damage this speaker", I'll request a 50W amplifier, not a 200W gorilla. Certainly, I can ultimately damage the speaker using the gorilla or a wimp, but it will be a little more work for me.
I understand that the general public would like to purchase a 200W speaker, a 100W amplifier, and be confident that they could not hurt anything. I wish that it could work that way.
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By the way, the above is how the amateur audio market deals with the physics of the situation. In professional sound contracting they talk about 70V systems, not 8-Ohm systems. It's the same physics, but the math is different (and, in my opinion, easier).
