The term "Special Effect" is borrowed from the Hero System, a super hero role playing game.
Each super power has a "Special Effect" - confusingly, this is not a description of how the power might be depicted on screen - but rather a deeper description of what's happening when the Character uses the power.
Take three example characters
The Human Torch's Special Effect is fire. His powers come from the ability to produce and control fire and heat.
Iceman's Special effect is Ice. He produces Ice and cold temperatures.
Hydro-Man's Special effect is Water. He can transform his body to water and he can produce and control water.
Hydro-Man is a villain so he attacks the Good Guys, Human Torch and Iceman.
Hydro-man has a power called "Energy Blast" - but the special effect is "A jet of water"
Iceman and Human Torch defend themselves with their powers. In both cases this the Force Field power.
In Iceman's case, he erects a wall of Ice between himself and Hydro-Man. and in Human-Torches' case he erects a wall of flame.
Although, in terms of game mechanics the attacks and defenses should be resolved identically - due to the special effect, the GM can alter the effects due to the special effects unerlying each power.
Human Torches defense falls quickly, because the water overwhelms his fire powers.
Iceman's defenses hold and even grow stronger because of the way water and Ice mix.
This is how the "Special Effect" affects the narrative.
In the case of Star Trek - the underlying special effect of any technology or phenomenon can affect the story. I think a story works better when the Special Effect is known and consistently applied by the writer.
Inflicting too much of this thought process directly on the Reader may not be fun, but properly emplyed the reader will subconsciously see the edges of the idea.