Shadows are one of the most prominent in-game stealth mechanics. It is important to know where they are and hide in them, so the hunters can't find you.
In Manhunt, to know if you're hidden or not, all you have to do is look at the Cash icon in your HUD. If it's gray, you're not hidden. If it's blue, you are hidden. Hunters will never find you in the shadow, even if they thoroughly examine it, unless they saw you get in it. If you tell The Tramp or The Journalist to stay put being near shadow, generally they will hide in it, and they lifebars on the HUD will change its colors from green to blue, meaning that hunters wouldn't be able to see them.
In Manhunt 2, if a hunter is suspicious, he might try to thoroughly inspect the shadow you are in, which prompts a minigame in which, if you fail, he'll spot you and grab you out of the shadow, forcing you to escape and find another shadow, or fight him face-to-face. Breaking a lamp will cause a shadow to appear, allowing you to hide from hunters.
In both games, hiding bodies in the shadows is an important feature so you can pass missions (like Awakening in Manhunt 2) and make the level easier (as hunters will use deadlier force and go with groups upon finding a dead comrade), however, this is completely optional.