The purpose of the power rating on the speaker is to tell you the level at which you may be doing damage to the equipment. However, despite, what others say, it is REALLY rare for a home audio user to actually use enough power to damage a well designed speaker. It is possible but not very likely.
It is true that a clipping amplifier can do damage to a voice coil but, again, clipping amplifiers in home audio applications are very rare because most amplifiers are way more powerful than what is actually needed to do the sound reproduction.
As an example, I keep a watt meter attached to one of the main speakers on my A/V system as a monitor. On very loud peaks like explosions in movies, I've seen the watt meter register a little over 20 watts. With dialogue it measures less than one watt. Most speakers have a power rating well beyond that as do most home audio amplifiers.
All these things you read about are really more important in pro audio where it takes massive power to fill large venues with sound. Filling a typical home family room with sound is pretty trivial. My powered mixer puts out 190 watts per channel into 8 ohms and is more than adequate to handle a church or a large hotel meeting room or even something the size of a high school auditorium. I might want to use up to 4 speakers for a high school auditorium but the mixer will handle that with no problem. I wouldn't use home audio speakers with that unit. They aren't tough enough. I use speakers that are designed to handle high power. For larger venues than that, I would need to haul out some seriously powerful amplification and lots of speakers.
I guess all I'm saying is that the power ratings on home audio speakers isn't important as long as you are using them in a home audio application. It might be fair to say that they are there so that some audio jockey doesn't try to fill an auditorium with sound using a pair of home audio book shelf speakers.
The sensitivity rating simply says that the speakers will deliver a test tone of the rated decibel level at a one meter listening distance with a 1 watt input signal. In other words, if I applied a 1000 hz test tone to a speaker rated at 95 db sensitivity with 1 watt of amplifier power, I would hear a 95 db signal at a one meter listening distance. 95 db is pretty loud, by the way. You can see why my A/V system measures well under a 1 watt for dialogue.
I hope this helps put things into perspective.