On overcast, cloudy days the light is nicely soft.
But it also makes it hard to make your subject stand out (pop) from all that soft light.
So you use supplemental lighting. Reflectors don't work very good on days like that so you use continuous, or strobed lighting.
Strobed lighting can be from an easily portable hot show strobe light (flash). If you can also use the strobe off the camera, all the better. You can crate some very interesting shadow modeling to really make your photographs look 'pro'.