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

Speed refers to transient response. 

The ability to follow musical transients (percussion, strings plucking, etc) closely. Both the attack and decay are important. 

Speakers with lighter, stiffer cone materials, and strong magnet structures are usually  have good speed.

Ribbon, electrostatic, and planar magnetic drivers tend to have good speed.

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. 

Can the impression of "speed" be adjusted with a multi-band parametric equalizer?

Impression being the operative word. Probably.
In reality, and measurably, no.

Fast with a speaker for me refers to low distortion resulting from minimal time lag due to inertia between signal and movement of the transducers as would be expected with a good combo of stronger magnets, precision machining and assembly of parts, and low mass driver and voice coil.

Result is the transducer/driver moves faster and more accurately than usual in response to the electric signal provided.

Efficiency is different.  That's the SPL produced in response to a standard electric signal.     Louder does not mean faster or less distortion in the time domain necessarily.