It's a Trail Renderer! I basically just attached the trail renderer to the sword, set the alpha to fade from 1-0 in its lifespan, and set the size to do the same. I also took some of the smoothing features off so it looks more cartoon-like to compliment the art (that's what is creating some of the rough angles).
I'm not sure what engine you're using, but I'm sure there should be a tutorial on it somewhere. If you're using Unity, I would recommend looking up "Blackthornprod - How to make cool trail effects - Unity Tutorial."