Efficiency = how much work it takes to give a certain result.
Example a more "Standard" efficiency speaker at around 90 db rating with 100 watt amp, will give a certain output DB at certain Gain level(volume)
Now a 93 db speaker will Give you the same output(theoretically) as the 90 db speaker, but will not take 100 watts it will take 50 watts... Less Work for the same results.
Go up to 96 db and essentially it will take 25 watts to do the same as the 93 db with 50 watts...
every 3 db increase in efficency should basically take half the work for similar results.. of course with everything else being equal, so its not like a 50 watt Threshold is not going to sound as powerfull as a 100 watt SANYO, as a matter of fact it would probably get slaugtered, but thats getting into a whole other issue.
But more watts is not necessarily better, however bigger amps regardless of the efficiency of the speakers can have more Headroom, another subject.
so don't go off thinking that a 100 db speaker will sound its best with a 10 watt amp, and be equal to a 90 db with a 200 watt amp in the sense of final results. its all about combination of equipment and really HOW good an amp is regardless of specs.
In a general sense more efficiency designed speaker could be better at lower level volume sound wise, due to they are more sensitive as well. And sure some big time wilson's or something still need some big time power regardless of the efficiency due to the larger woofers and desired SPL's. And they can work fine with smaller more refined amps as well depending on the rest of the requirments of one's listening environment, preference, and pocket book.
Sorry if I confused matters at all and correct any of the above as seen fit.