Basically, the higher the sensitivity rating the louder the speaker will be with less power from your amplifier/receiver. I believe this figure is determined by putting a 1Khz signal at 1 watt through the speaker and measuring the speaker's output from a one meter distance. There may be other elements involved, but that's my understanding.
That link is a fine treatment on the subject. You also asked if higher sensitivity is better and the answer to that is no. The worlds finest speakers are all over the map when it comes to sensitivity and efficiency, so this is not at all a gauge by which one can judge a speaker's sound or quality. (Although for various reasons the designs some tend to favor happen to typically be highly efficient, while the ones others favor are not.)
The efficiency and sensitivity numbers are there to allow one to determine how much power will be needed to play the speakers of your choice at your required listening levels.
To state that in a different way - a speaker's sensitivity only tells you how easy or difficult it will be for your amplifier (or, any given amplifier) to drive it. It tells you absolutely nothing about how it sounds. If "everything else were the same", then yes, higher sensitivity is better. However, you'll be really hard pressed to find two speakers which are identical except for their sensitivity.
So, basically, it becomes more important if you already have an amplifier, or have decided on an amplifier, because then you need to pick speakers that your amp can drive. Otherwise, you don't really need to worry about it too much, just make sure you pick a suitable amp to drive it with.
Generally listen to speakers that you like the sound of and pay attention to the sensitivity ratings. If you don't have lots of watts, then select from speakers with higher sensivity. There is a lot more to a speakers sound quality than sensivity, but there are enough speakers with high sensitivity (89dB or higher) that you can find something good. If you only have a 40 watt per channel amplifier and you like bass, don't buy speakers with a sensitivity rating of 82 dB for example
I find that higher sensitivity is always advantageous in HT ,WHERE DYNAMIC RANGE IS IMPORTANT. Also ,if you prefer music with impact. If you like to play music at lower listening levels and want the speakers to still produce a good sound with the limited juice ,then high efficiency also helps. Of course ,if you have VERY powerful amps than you can drive less efficiant speakers (of couse,more efficiant ones would still play louder)....is there a pattern here?
Yeah, it seems that the more efficient the better for volume and dynamics of course, but its not a fast and hard rule. Some actually like the sound of inefficient speakers more than efficient ones. Not to generalize all speakers with similar sensitivity ratings, but I mean to say that some people prefer the sound of speakers with lower efficiencies. I haven't compared enough speakers yet. I like efficient speakers for obvious reasons.
Walt, excellent point. Never occurred to me to specify that efficiency is just a number that tells you how much power the speaker needs, not how it sounds. Damn assumptions :p) I've added the clarifcation to my post in the other thread.