To slacken is to loosen the tension on or tightness of something. If you slacken the clothesline any more, the clothes will be on the ground next time you hang out the wash.
Slacken, in the "to loosen" sense, can also be used figuratively. Because you have been so responsible, we're going to slacken the rules about curfew on non-school nights and let you stay out an hour later. Slacken also means to slow down or make less active. If you are in a sprint race, you won't want to slacken your pace until after you cross the finish line or you might not win.