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

Erik, yes speakers interact with the room but that has nothing to do with the transient response on the 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. 
Andy, resolution and transient response are very closely related. By dynamic I do not mean loud. I mean snap.

Andy, all I am saying is that the more revealing a speaker is the more sensitive it is to defects up stream such as a miss tracking cartridge or distorting amplifier. ESLs, ribbons and horns are frequently blamed for problems elsewhere in the system. Not that some very good dynamic speakers might get caught up in this.  

resolution and transient response are very closely related. By dynamic I do not mean loud. I mean snap.

Yes, but they may not be one to one exact. A high end paper driver may have more resolution and a low end aluminum driver may have more transient but the aluminum driver may not have the resolution of the paper driver.

Snap could mean a lot of thing. A speaker may have a lot of snap but it does not mean it has a lot of resolution. I can fine tune my speaker to have tighter bass and extra energy in the higher frequency to give it more snap but it may not have more resolution.

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