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

In my experience 'faster sounding' loudspeakers do tend to sound lighter in bass compared to slower designs. They simply don't bother getting involved in the arduous and problematic task of reaching down to seriously low frequencies.

Nothing gives me the impression of 'slowness' in a loudspeaker as much as bass overhang where the bass rhythms simply go to pot and hopelessly lag behind. 

Bass resonance factors also have an effect on the transient response of the cone as well as cabinet colorations. 

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.