The so-called "Sin City effect" is a color-correction technique in which a range of colors is left saturated with color while the rest of an image (can be still or video) is completely desaturated to black and white. The effect is called the "Sin City effect" because it was used widely in Robert Rodriguez' film "Sin City."
But you don't need a Hollywood post-production budget to do it. In fact, all you need is Final Cut Pro and a few minutes.
Check out the video below and stylize your next project: