In an ideal world, when reproducing sound, we would want to drive the air with the lightest medium possible and that is where the "massless" speaker comes in. A massless transducer makes sound using only the air itself and is alone in being electroacoustic. This could be by converting the air to a plasma, driving the air directly by electrons/ions from high voltage sources or from any other method that does not involve the movement of a solid or liquid and the transition from that to the gas (air).
You can quickly argue that none of these speakers are massless because air, ions, electrons and plasma have mass. Yes, in physics that is correct. You can stop here and disagree with the usage of massless now. Air has mass and weighs around 1.29kg per cubic metre depending on temperature, pressure and humidity. Plasma and ion charged air is similar. However, words often have different meanings when used in different fields.
Air is the medium in which we hear sound, you can't hear it in a vacuum. So when used in relation to audio, a massless speaker is one that has no mass relative to air and the sound is produced with no added net mass.
These devices have the inherent benefit of having no moving parts. With all other loudspeaker designs there is a spring-mass-damped system that has inertia that must affect the sound and will always have resonant frequencies. In addition there is a solid to air interface which can scatter and absorb energy and add reflections to the overall acoustic system which is undesirable. A similar term sometimes used is inertialess, without mass there is no inertia to overcome.
There is one possible amendment to this. A number of massless speaker designs use a horn to couple the output with the air. This introduces additional air mass into the system and a horn has its own spring-mass-damped system and resonances. Commercial designs such as Klein's Ionophone and the Lanch Audio's Corona use horn loading but it is by no means essential as shown in the Hill Plasmatronic and Magnat Mp series. There are many prototype plasma and ionic designs that have been demonstrated and work without horns.
So we could call these massless as an overall description. Referring to them all as plasma, ionic or similar is not accurate as those are sub-categories with different physical principles at work. Massless seems a reasonably easy to use term to encompass all of them.
Perhaps there are more accurate alternatives, such as inertialess, solid-state, electro-fluid-dynamic (EFD), electrohydrodynamic (EHD), electroconvective or electroaerodynamic.
For now we'll stick with massless here. More about naming.