How do you know what a good speaker is?

To me a good speaker is one that I really enjoy listening to and equally as important I want a speaker that will sound better with each upgrade I can afford to add, whether that is a better amplifier preamplifier Dac even a cable upgrade. I want a speaker that will sound mellow with a mellow sounding amplifier or sound bright with a bright sounding amplifier. If the amp has higher resolution I want to hear it. If the amp is not very good I want to hear that. 

That has been my experience and it works for me.

Speakers are First Personal because everyones ears are different.
They should also have Transparency.
A Speaker should sound like the sound is Not Coming from them.
They should sound like you are listening in Person.

I think Magnepan and Martin-Logan engineers who eschew boxes and simplify the crossover to first order: a capacitor to the tweeter and a coil to the mid-bass regard the very complicated crossovers, notch filters that attempt to tame the wild variability of impedance with respect to frequency and the bracing of cabinets to try to minimize the effect of a speaker varying the pressure on a cabinet as what John Northrup called "inventing rubber gloves for leaky fountain-pens." These simplifications and auditioning made my choice very easy. But these first-order crossover designs and their planar diaphragms take extra power to duplicate the volume of the orchestra and singers in an opera house. I also like the simplicity of the single ended triode amplifier which, in the case of the usual choices like the 300-B, are not powerful enough. So if you want both the open purity of a planar speaker and that SET refinement you have to drive the speakers with something like an 822-A single ended triode amplifier, which is not as difficult as you think to design and build.   

A good speaker for low volume classics and jazz?  I have been trying since 1970 for a low volume speaker with decent bass and imagining.  I am not an expert by any means.  Here is what works for me, when listening and conversing.  1 pair of Magnepan MMG, 1 pair of Magnepan DWM, 1 pair of Heil AMT large transformers.  Each DWM is used in mono mode for a 2 ohm load.  The AMT is wired to one output of the DWM and then a 10 watt 4 ohm resistor from + to - and a 2.2 capacitor to the AMT.  This presents a 1.8 ohm load to the amplifier.  Two Dennon 6600 monoblocks are the amplifiers used.  The living room is 15 by 19, the speakers are 5 feet from the wall.I have musician friends over to listen.  The clarity and imaging seem superb at any volume, imo.  All speakers were purchased used, except for the DWMs.  The DWM is only rated to 40 hz.
In the search for a compatible subwoofer, happened on a Distributed Bass site.  Yesterday, 2 kicker 10's, each in a sealed 2 cubic foot enclosure were placed woofer to wall with 3/4 inches of clearance space.  Power is from old mosfet MTX/Soundcraftsman s800 in mono, the two present the amp with a 1.8 ohm load.  My DBX 223XL gave up yesterday, so far no external xover.  It sounds very good to me.  I solicit honest opinions from my visitor friends.  My first decent speakers were ESS AMT4's in 1973. 

First off I agree with those who have stated that the best pair of speakers are the ones that ultimately put a smile on your face.

That said, Specs - especially Frequency Response should only be used as a guide as to how to filter down your purchasing decisions. 

MIT and NASA concur that the natural environment in which humans process sound has a Frequency Response of 15Hz to 150Khz. 

The questions that you need to answer for yourself is how relevant is that information to you? Are you after the purest sound replication or are you more into convenience or aesthetics? What kind of investment are you willing to make to accomplish your goals?  There are no wrong answers.

If you are truly dedicated to pure sound replication then your goal should be to try to work towards creating an environment as close to 15Hz to 150Khz as you can get. The listed specs from manufacturers should be able to narrow this field down for you. It will take actual listening on your part to decide which one replicates the right violin, cello, piano, human voice for you.  

I know one person who does not believe MIT and NASA. The set up he has is good enough for him and his needs.

Another person believes in the findings, however just likes the sweet mid range sound staging that EL 34 tubes create and has worked towards accomplishing those goals.

There are only a handful of companies that list that they have speakers that match the 15Hz-150Khz spec. These are all listed at astronomical prices.

Another audiophile I know does believe in the MIT/NASA findings and has the scratch to throw $250K++ just at speakers alone. However he has learned that the speakers are just one ingredient in creating this environment as there several other components to factor in.