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

The issue of loudspeaker speed (like almost everything else about loudspeakers) seems to be endlessly complex.

Here's an interesting interview with Allan Hendry of Monopulse loudspeakers.

https://www.monopulse.co.uk/quest.htm

If what he's saying is correct, and I don't have enough knowledge to know any better, then many (if not all!) two way designs could be seriously flawed when it comes to speed, phase and integration issues.

Transient response, certainly, as has been pointed out by others, sonically perceived as a lack of smear/crispness, unforced clarity and liquidity. Usually, not least through quality all-horns, I find it linked to uninhibited dynamics as well (or: ease of "explosivity," felt as a startling experience), coupled to (at least as a partially responsible aspect) a pronounced degree of low volume level "ignition," whereby music comes alive quite easily at lower SPL's. 

Hold on Andy. That is a mistake. Yes they are all transducers but their ability to function in air is quite different. ESLs and horns are a better impedance match to air and transmit sound waves more efficiently. Dynamic drivers have to work harder to get the same results. ESLs work entirely differently than conventional speakers. First, there are no magnets. ESLs are capacitors conventional drivers are not and represent an entirely different load to the amplifier. Designed correctly their transient response is superior to conventional drivers because the moving system has far less inertia and is a better impedance match to air.
Planar speakers are somewhere in between. IMHO in spite of the compromises you have to make ESLs rule as long as you can make them. I have personally not heard a conventional speaker sound as convincing. Some say well designed horns can do it. But I am still waiting to hear one that does. 

cd318, quite a long marketing dissertation for a easily solved problem. All he says about our hearing is correct. Our ears are primarily location detection devices. They evolved to locate danger. His analysis of speakers is correct. This is the major problem for horn speakers like the K horn. The drivers are at significantly different distances from you ears.
The "easy" solution is to use one driver and no cross over. Not so easy.
The only transducer type that has been able to do this successfully is the full range ESL. Trying to do this in the analog domain with conventional drivers is difficult and only really effective at one location. At higher frequencies say the midrange to tweeter crossover it is more difficult to match things up then at much lower frequencies with longer "slower" wave lengths like a sub woofer crossover. 

All speakers have mass and inertia, because they are mechanical devices pushing air. This means the "thing" in the speaker that moves the air will never respond instantaneously to what the amplifier throws at it (i.e. be fast).

Electrostatics is one technology that is 'faster' than most.

Large cone speakers (woofers) driven by electromagnetic coils are slow because the cones are heavy and electromagnets have electrical inertia. Electromagnets resist any signal feed to them from an amplifier and they return a signal back to the amplifier (back-EMF).

Low impedance output stages on amplifiers are important because they help 'dampen' the back-EMF, effectively stiffening the cone speaker. 

Tweeters and electrostatic panels tend to have light mass - they respond faster than woofers (bass speakers). Hence why Martin Logans can sound like the bass is slower than the panel.

Some speaker designers used to put the tweeters physically behind the plane of the woofer to try and accomodate the slower response of the woofer. Perhaps the B&W 800's do this?

Any two or three way speaker will struggle with phasing. Two way speakers often sound cleaner because of less speaker phase issues and the cross-over networks are simpler. Cross-over networks that use inductors and capacitors can potentially introduce phasing issues.

Quad electrostatics always sounded great because they were basically a single cone speaker. Bass was not great though. It was interesting playing Telarc's 1812 CD through Quad ESL 2905's.