What does the term "Speed" mean in a speaker?

Mike, unfortunately regular dynamic drivers are a poor impedance match to air. They have to work much harder to get the job done. ESLs and Horns do not have this problem to near the degree.
ESLs and horns are generally described as being very detailed. They also have better transient response, association or causation. I would say the later. Yes, a speaker with a lighter moving system could have better transient response assuming the motor was designed correctly.

there is a general rule, and then there are specific situations and execution. sure, dynamic cones have their advantages and disadvantages. so you need to execute over-the-top to overcome the disadvantages.

in my case that way they did it was high efficiency, and overkill with driver surface. you have -4- 15" powered subwoofer drivers per channel in a separate tower for under 40hz, and -4- 11" ceramic matrix woofer passive drivers for 40hz-250hz. this is considerably more driver surface for the mid-bass than any other dynamic cone speaker. and it’s an easy amp load of 97 db, 7 ohm. visitors who hear it exactly comment that it sounds like a planer or stat it’s so seamless and fast. yet it has the weight of a dynamic driver and since it’s an integrated design it is coherent with the lowest octaves from the bass tower too.

http://www.evolutionacoustics.com/loudspeakers/mm-series/mmseven/

When a speaker has "speed" it's approaching the sound of real, life like, sound. At times it can be so convincing, that it makes you forget about the other shortcomings it may have, like the actual soundstage, imaging, etc.

You'll notice it at first with a particular instrument or vocalist. Then you'll listen for other cues and with other recordings to see if it can be replicated.

It may not be done in an across the board accounting but at least you'll know what your speakers are capable of, given the right recording.

All the best,
Nonoise

From my time in the audio hobby and profession,  I feel speaker "speed" has much to do with the response time in moving with the very first note/electrical impulse.  The trailing edge of a note is easier for a transducer as it is already in motion.  However the leading edge begins with the speaker/transducer at "rest", and the possibility of the transducer being slower than the electrical impulse being sent to the transducer.  (sorry for the "transducer" word, but I do not put electrostatic and planer speakers in the same category as push-pull standard types of speakers).  

Interesting question and answers. 

When a speaker has "speed" it's approaching the sound of real, life like, sound

Designing speaker is a compromise - some are optimized for speed (dynamic), or soundstage, or musicality.  Some $80K speakers can have a huge soundstage but lack musicality.  Some are optimized for speed but soundstage may lack bloom.  And so on ...

I do not put electrostatic and planer speakers in the same category as push-pull standard types of speakers

That may be true, but conventional drivers are transducers nevertheless - they convert electrical energy to mechanical energy hence by definition they are transducers. And fundamentally there’s not much difference between electrostatic panels and conventional drivers.  They might be different but not fundamentally.